mirror of
https://github.com/3b1b/manim.git
synced 2025-09-19 04:41:56 +00:00
Up to the pont where phase space is introduced
This commit is contained in:
Grant Sanderson
parent
0b56d6f311
commit
9cdf35475d
5 changed files with 348 additions and 97 deletions
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@ -1,6 +1,7 @@
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from active_projects.ode.part1.pendulum import *
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from active_projects.ode.part1.staging import *
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from active_projects.ode.part1.pi_scenes import *
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from active_projects.ode.part1.wordy_scenes import *
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OUTPUT_DIRECTORY = "ode/part1"
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ALL_SCENE_CLASSES = [
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@ -25,4 +26,7 @@ ALL_SCENE_CLASSES = [
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SubtleAirCurrents,
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DefineODE,
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ODEvsPDEinFrames,
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ProveTeacherWrong,
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SetAsideSeekingSolution,
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VisualizeStates,
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]
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@ -103,6 +103,95 @@ class FormulasAreLies(PiCreatureScene):
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return You().flip().to_corner(DR)
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class NewSceneName(Scene):
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class ProveTeacherWrong(TeacherStudentsScene):
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def construct(self):
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pass
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tex_config = {
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"tex_to_color_map": {"{\\theta}": BLUE}
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}
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func = TexMobject(
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"{\\theta}(t)", "=",
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"\\theta_0", "\\cos(\\sqrt{g / L} \\cdot t)",
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**tex_config,
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)
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d_func = TexMobject(
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"\\dot {\\theta}(t)", "=",
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"-\\left(\\sqrt{g / L}\\right)",
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"\\theta_0", "\\sin(\\sqrt{g / L} \\cdot t)",
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**tex_config,
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)
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dd_func = TexMobject(
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"\\ddot {\\theta}(t)", "=",
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"-\\left(g / L\\right)",
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"\\theta_0", "\\cos(\\sqrt{g / L} \\cdot t)",
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**tex_config,
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)
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ode = TexMobject(
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"\\ddot {\\theta}({t})", "=",
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"-\\mu \\dot {\\theta}({t})",
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"-{g \\over L} \\sin\\big({\\theta}({t})\\big)",
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**tex_config,
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)
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arrows = [TexMobject("\\Downarrow") for x in range(2)]
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VGroup(func, d_func, dd_func, ode, *arrows).scale(0.7)
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teacher = self.teacher
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you = self.students[2]
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self.student_thinks(ode)
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you.add_updater(lambda m: m.look_at(func))
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self.teacher_holds_up(func)
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self.wait()
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group = VGroup(arrows[0], d_func, arrows[1], dd_func)
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group.arrange(DOWN)
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group.move_to(func, DOWN)
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arrow = Arrow(
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group.get_corner(UL),
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ode.get_top(),
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path_arc=PI / 2,
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)
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q_marks = VGroup(*[
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TexMobject("?").scale(1.5).next_to(
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arrow.point_from_proportion(a),
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UP
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)
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for a in np.linspace(0.2, 0.8, 5)
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])
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cycle_animation(VFadeInThenOut(
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q_marks,
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lag_ratio=0.2,
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run_time=4,
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rate_func=squish_rate_func(smooth, 0, 0.5)
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))
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self.play(
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func.next_to, group, UP,
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LaggedStartMap(
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FadeInFrom, group,
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lambda m: (m, UP)
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),
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teacher.change, "guilty",
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you.change, "sassy",
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)
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rect = SurroundingRectangle(
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VGroup(group, func)
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)
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dashed_rect = DashedVMobject(rect, num_dashes=75)
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animated_rect = AnimatedBoundary(dashed_rect, cycle_rate=1)
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self.wait()
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self.add(animated_rect, q_marks)
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self.play(
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ShowCreation(arrow),
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# FadeInFromDown(q_mark),
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self.get_student_changes("confused", "confused")
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)
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self.wait(4)
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self.change_student_modes(
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*3 * ["pondering"],
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self.teacher.change, "maybe"
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)
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self.wait(8)
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@ -14,3 +14,19 @@ class You(PiCreature):
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CONFIG = {
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"color": BLUE_C,
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}
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def get_ode():
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tex_config = {
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"tex_to_color_map": {
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"{\\theta}": BLUE,
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"{t}": WHITE,
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}
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}
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ode = TexMobject(
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"\\ddot {\\theta}({t})", "=",
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"-\\mu \\dot {\\theta}({t})",
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"-{g \\over L} \\sin\\big({\\theta}({t})\\big)",
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**tex_config,
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)
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return ode
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@ -47,39 +47,6 @@ class VectorFieldTest(Scene):
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self.wait(10)
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class SmallAngleApproximationTex(Scene):
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def construct(self):
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approx = TexMobject(
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"\\sin", "(", "\\theta", ") \\approx \\theta",
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tex_to_color_map={"\\theta": RED},
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arg_separator="",
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)
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implies = TexMobject("\\Downarrow")
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period = TexMobject(
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"\\text{Period}", "\\approx",
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"2\\pi \\sqrt{\\,{L} / {g}}",
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**Lg_formula_config,
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)
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group = VGroup(approx, implies, period)
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group.arrange(DOWN)
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approx_brace = Brace(approx, UP, buff=SMALL_BUFF)
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approx_words = TextMobject(
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"For small $\\theta$",
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tex_to_color_map={"$\\theta$": RED},
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)
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approx_words.scale(0.75)
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approx_words.next_to(approx_brace, UP, SMALL_BUFF)
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self.add(approx, approx_brace, approx_words)
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self.play(
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Write(implies),
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FadeInFrom(period, LEFT)
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)
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self.wait()
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class FollowThisThread(Scene):
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CONFIG = {
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"screen_rect_style": {
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@ -165,64 +132,6 @@ class FollowThisThread(Scene):
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self.wait()
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class StrogatzQuote(Scene):
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def construct(self):
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law_words = "laws of physics"
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language_words = "language of differential equations"
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author = "-Steven Strogatz"
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quote = TextMobject(
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"""
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\\Large
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``Since Newton, mankind has come to realize
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that the laws of physics are always expressed
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in the language of differential equations.''\\\\
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""" + author,
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alignment="",
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arg_separator=" ",
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substrings_to_isolate=[law_words, language_words, author]
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)
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law_part = quote.get_part_by_tex(law_words)
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language_part = quote.get_part_by_tex(language_words)
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author_part = quote.get_part_by_tex(author)
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quote.set_width(12)
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quote.to_edge(UP)
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quote[-2].shift(SMALL_BUFF * LEFT)
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author_part.shift(RIGHT + 0.5 * DOWN)
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author_part.scale(1.2, about_edge=UL)
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movers = VGroup(*quote[:-1].family_members_with_points())
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for mover in movers:
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mover.save_state()
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disc = Circle(radius=0.05)
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disc.set_stroke(width=0)
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disc.set_fill(BLACK, 0)
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disc.move_to(mover)
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mover.become(disc)
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self.play(
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FadeInFrom(author_part, LEFT),
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LaggedStartMap(
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# FadeInFromLarge,
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# quote[:-1].family_members_with_points(),
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Restore, movers,
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lag_ratio=0.005,
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run_time=2,
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)
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# FadeInFromDown(quote[:-1]),
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# lag_ratio=0.01,
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)
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self.wait()
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self.play(
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Write(law_part.copy().set_color(YELLOW)),
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run_time=1,
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)
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self.wait()
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self.play(
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Write(language_part.copy().set_color(BLUE)),
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run_time=1.5,
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)
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self.wait(2)
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class ShowGravityAcceleration(Scene):
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def construct(self):
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self.add_gravity_field()
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@ -472,6 +381,7 @@ class DefineODE(Scene):
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self.show_value_slope_curvature()
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self.write_ode()
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self.show_second_order()
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self.show_higher_order_examples()
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self.show_changing_curvature_group()
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def add_graph(self):
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@ -494,8 +404,8 @@ class DefineODE(Scene):
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de_word.to_edge(UP)
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equation = TexMobject(
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"\\ddot \\theta({t}) = "
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"-\\mu \\dot \\theta({t})"
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"\\ddot \\theta({t})", "=",
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"-\\mu \\dot \\theta({t})",
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"-{g \\over L} \\sin\\big(\\theta({t})\\big)",
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tex_to_color_map={
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"\\theta": BLUE,
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@ -693,6 +603,7 @@ class DefineODE(Scene):
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v_line, slope_line, curve, dot
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)
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self.curvature_group_labels = VGroup(thetas, words)
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self.fake_graph = graph
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def write_ode(self):
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equation = self.equation
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@ -761,12 +672,102 @@ class DefineODE(Scene):
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self.ode_initials = ode_initials
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def show_second_order(self):
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pass
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so = TextMobject("Second order")
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so.scale(1.4)
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ode = self.ode_initials
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ode.generate_target()
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group = VGroup(so, ode.target)
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group.arrange(RIGHT, aligned_edge=DOWN)
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group.to_edge(UP, buff=MED_SMALL_BUFF)
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second_deriv = self.equation[:5]
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self.play(
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Write(so),
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MoveToTarget(ode),
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)
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self.wait()
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self.play(FocusOn(second_deriv))
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self.play(
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Indicate(second_deriv, color=RED),
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)
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self.wait()
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self.second_order_word = so
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def show_higher_order_examples(self):
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main_example = VGroup(
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self.second_order_word,
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self.ode_initials,
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self.equation
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)
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tex_config = {"tex_to_color_map": {"{x}": BLUE}}
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example3 = VGroup(
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TextMobject("Third order ODE"),
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TexMobject(
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"\\dddot {x}(t) + \\dot {x}(t)^2 = 0",
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**tex_config,
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)
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)
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example4 = VGroup(
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TextMobject("Fourth order ODE"),
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TexMobject(
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"\\ddddot {x}(t) +",
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"a\\dddot {x}(t) \\dot {x}(t) + ",
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"b \\ddot {x}(t) {x}(t)",
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"= 1",
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**tex_config,
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)
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)
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for example in [example3, example4]:
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example[0].scale(1.2)
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example.arrange(DOWN, buff=MED_LARGE_BUFF)
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example.to_edge(UP, buff=MED_SMALL_BUFF)
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self.play(
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FadeOut(main_example),
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FadeIn(example3),
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)
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self.wait(2)
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self.play(
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FadeOut(example3),
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FadeIn(example4),
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)
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self.wait(2)
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self.play(
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FadeOut(example4),
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FadeIn(main_example),
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)
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self.wait(2)
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def show_changing_curvature_group(self):
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pass
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t_tracker = self.t_tracker
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curvature_group = self.curvature_group
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labels = self.curvature_group_labels
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graph = VMobject()
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graph.pointwise_become_partial(
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self.fake_graph,
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0.25, 1,
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)
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dashed_graph = DashedVMobject(graph, num_dashes=100)
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dashed_graph.set_stroke(GREEN, 1)
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self.play(FadeOut(labels))
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self.add(dashed_graph, curvature_group)
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self.play(
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t_tracker.set_value, 10,
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ShowCreation(dashed_graph),
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run_time=15,
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rate_func=linear,
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)
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self.wait()
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class ODEvsPDEinFrames(Scene):
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def construct(self):
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pass
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class VisualizeStates(Scene):
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def construct(self):
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pass
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|
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141
active_projects/ode/part1/wordy_scenes.py
Normal file
141
active_projects/ode/part1/wordy_scenes.py
Normal file
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@ -0,0 +1,141 @@
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from big_ol_pile_of_manim_imports import *
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from active_projects.ode.part1.shared_constructs import *
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class SmallAngleApproximationTex(Scene):
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def construct(self):
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approx = TexMobject(
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"\\sin", "(", "\\theta", ") \\approx \\theta",
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tex_to_color_map={"\\theta": RED},
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arg_separator="",
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)
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implies = TexMobject("\\Downarrow")
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period = TexMobject(
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"\\text{Period}", "\\approx",
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"2\\pi \\sqrt{\\,{L} / {g}}",
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**Lg_formula_config,
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)
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group = VGroup(approx, implies, period)
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group.arrange(DOWN)
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approx_brace = Brace(approx, UP, buff=SMALL_BUFF)
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approx_words = TextMobject(
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"For small $\\theta$",
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tex_to_color_map={"$\\theta$": RED},
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)
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approx_words.scale(0.75)
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approx_words.next_to(approx_brace, UP, SMALL_BUFF)
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self.add(approx, approx_brace, approx_words)
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self.play(
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Write(implies),
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FadeInFrom(period, LEFT)
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)
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self.wait()
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class StrogatzQuote(Scene):
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def construct(self):
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law_words = "laws of physics"
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language_words = "language of differential equations"
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author = "-Steven Strogatz"
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quote = TextMobject(
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"""
|
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\\Large
|
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``Since Newton, mankind has come to realize
|
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that the laws of physics are always expressed
|
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in the language of differential equations.''\\\\
|
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""" + author,
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alignment="",
|
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arg_separator=" ",
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substrings_to_isolate=[law_words, language_words, author]
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)
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law_part = quote.get_part_by_tex(law_words)
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language_part = quote.get_part_by_tex(language_words)
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author_part = quote.get_part_by_tex(author)
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quote.set_width(12)
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quote.to_edge(UP)
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quote[-2].shift(SMALL_BUFF * LEFT)
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author_part.shift(RIGHT + 0.5 * DOWN)
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author_part.scale(1.2, about_edge=UL)
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movers = VGroup(*quote[:-1].family_members_with_points())
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for mover in movers:
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mover.save_state()
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disc = Circle(radius=0.05)
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disc.set_stroke(width=0)
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disc.set_fill(BLACK, 0)
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disc.move_to(mover)
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mover.become(disc)
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self.play(
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FadeInFrom(author_part, LEFT),
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LaggedStartMap(
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# FadeInFromLarge,
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# quote[:-1].family_members_with_points(),
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Restore, movers,
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lag_ratio=0.005,
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run_time=2,
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)
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# FadeInFromDown(quote[:-1]),
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# lag_ratio=0.01,
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)
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self.wait()
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self.play(
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Write(law_part.copy().set_color(YELLOW)),
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run_time=1,
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||||
)
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self.wait()
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self.play(
|
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Write(language_part.copy().set_color(BLUE)),
|
||||
run_time=1.5,
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||||
)
|
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self.wait(2)
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||||
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||||
|
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class SetAsideSeekingSolution(Scene):
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def construct(self):
|
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ode = get_ode()
|
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ode.to_edge(UP)
|
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q1 = TextMobject("Find an exact solution")
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q1.set_color(YELLOW)
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q2 = TexMobject(
|
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"\\text{What is }", "\\theta", "(t)",
|
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"\\text{'s personality?}",
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tex_to_color_map={"\\theta": BLUE},
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||||
arg_separator="",
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||||
)
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||||
theta = q2.get_part_by_tex("\\theta")
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||||
|
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for q in q1, q2:
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q.scale(1.5)
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q.next_to(ode, DOWN, MED_LARGE_BUFF)
|
||||
eyes = Eyes(theta, height=0.1)
|
||||
|
||||
self.add(ode)
|
||||
self.add(q1)
|
||||
self.wait()
|
||||
self.play(
|
||||
q1.scale, 0.3,
|
||||
q1.to_corner, UR, MED_SMALL_BUFF,
|
||||
)
|
||||
self.play(FadeInFrom(q2, DOWN))
|
||||
self.play(
|
||||
eyes.blink,
|
||||
rate_func=lambda t: smooth(1 - t),
|
||||
)
|
||||
self.play(eyes.look_at, q2.get_left())
|
||||
self.play(eyes.look_at, q2.get_right())
|
||||
self.play(
|
||||
eyes.blink,
|
||||
rate_func=squish_rate_func(there_and_back)
|
||||
)
|
||||
self.wait()
|
||||
self.play(
|
||||
eyes.change_mode, "confused",
|
||||
eyes.look_at, ode.get_left(),
|
||||
)
|
||||
self.play(
|
||||
eyes.blink,
|
||||
rate_func=squish_rate_func(there_and_back)
|
||||
)
|
||||
Loading…
Add table
Reference in a new issue