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AnalyzePendulumForce

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This commit is contained in:
Grant Sanderson
2019-03-21 10:52:43 -07:00
parent 84a950425c
commit 573abe82b8
2 changed files with 225 additions and 30 deletions
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1
active_projects/ode/all_part1_scenes.py
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@ -18,5 +18,6 @@ ALL_SCENE_CLASSES = [
StrogatzQuote,
# Something...
ShowGravityAcceleration,
AnalyzePendulumForce,
BuildUpEquation,
]

254
active_projects/ode/part1/pendulum.py
View File

@ -110,17 +110,21 @@ class Pendulum(VGroup):
return self
def add_theta_label(self):
label = self.theta_label = TexMobject("\\theta")
label.set_height(self.theta_label_height)
self.theta_label = always_redraw(self.get_label)
self.add(self.theta_label)
def update_label(l):
top = self.get_fixed_point()
arc_center = self.angle_arc.point_from_proportion(0.5)
vect = arc_center - top
vect = normalize(vect) * (1 + self.theta_label_height)
l.move_to(top + vect)
label.add_updater(update_label)
self.add(label)
def get_label(self):
label = TexMobject("\\theta")
label.set_height(min(
self.theta_label_height,
self.angle_arc.get_width(),
))
top = self.get_fixed_point()
arc_center = self.angle_arc.point_from_proportion(0.5)
vect = arc_center - top
vect = normalize(vect) * (1 + self.theta_label_height)
label.move_to(top + vect)
return label
#
def get_theta(self):
@ -841,12 +845,12 @@ class VeryLowAnglePendulum(LowAnglePendulum):
}
class BuildUpEquation(MovingCameraScene):
class AnalyzePendulumForce(MovingCameraScene):
CONFIG = {
"pendulum_config": {
"length": 5,
"top_point": 3 * UP,
"initial_theta": 45 * DEGREES,
"top_point": 3.5 * UP,
"initial_theta": 60 * DEGREES,
},
"g_vect_config": {
"length_multiple": 0.25,
@ -859,15 +863,12 @@ class BuildUpEquation(MovingCameraScene):
self.add_pendulum()
self.show_constraint()
self.break_g_vect_into_components()
self.show_angle_geometry()
self.show_gsin_formula()
self.show_acceleration_at_different_angles()
self.show_angle_geometry()
self.ask_about_what_to_do()
self.show_velocity_and_position()
self.show_derivatives()
self.show_equation()
self.talk_about_sine_component()
self.add_air_resistance()
# TODO, indication of theta?
# pendulum movement? Things like that?
def add_pendulum(self):
self.pendulum = Pendulum(**self.pendulum_config)
@ -922,9 +923,9 @@ class BuildUpEquation(MovingCameraScene):
ShowCreation(arc)
)
arcs.add(arc)
pendulum.clear_updaters()
self.wait()
self.play(FadeOut(arc))
self.theta_tracker = theta_tracker
def break_g_vect_into_components(self):
g_vect = self.g_vect
@ -945,25 +946,218 @@ class BuildUpEquation(MovingCameraScene):
color=self.perp_line_color,
))
self.play(
ShowCreation(g_vect.component_lines),
)
self.play(ShowCreation(g_vect.component_lines))
self.play(GrowArrow(g_vect.tangent))
self.wait()
self.play(GrowArrow(g_vect.perp))
self.wait()
def show_angle_geometry(self):
g_vect = self.g_vect
def show_gsin_formula(self):
pass
g_vect = self.g_vect
g_word = self.g_word
g_word.clear_updaters()
g_term = self.g_term = TexMobject("-g")
g_term.add_updater(lambda m: m.next_to(
g_vect,
RIGHT * np.sign(self.pendulum.get_theta()),
SMALL_BUFF
))
def create_vect_label(vect, tex, direction):
label = TexMobject(tex)
label.set_stroke(BLACK, 5, background=True)
label.add_background_rectangle()
label.scale(0.7)
max_width = 0.9 * vect.get_length()
if label.get_width() > max_width:
label.set_width(max_width)
angle = vect.get_angle()
angle = (angle + PI / 2) % PI - PI / 2
label.next_to(ORIGIN, direction, SMALL_BUFF)
label.rotate(angle, about_point=ORIGIN)
label.shift(vect.get_center())
return label
g_sin_label = always_redraw(lambda: create_vect_label(
g_vect.tangent, "-g\\sin(\\theta)", UP,
))
g_cos_label = always_redraw(lambda: create_vect_label(
g_vect.perp, "-g\\cos(\\theta)", DOWN,
))
self.play(ReplacementTransform(g_word, g_term))
self.wait()
self.play(TransformFromCopy(g_term, g_sin_label))
self.wait()
self.play(TransformFromCopy(g_term, g_cos_label))
self.wait()
self.g_sin_label = g_sin_label
self.g_cos_label = g_cos_label
def show_acceleration_at_different_angles(self):
pass
to_fade = VGroup(
self.g_cos_label,
self.g_vect.perp,
self.g_vect.component_lines,
)
self.play(to_fade.set_opacity, 0.25)
for mob in to_fade:
mob.add_updater(lambda m: m.set_opacity(0.25))
get_theta = self.pendulum.get_theta
theta_decimal = DecimalNumber(include_sign=True)
theta_decimal.add_updater(lambda d: d.set_value(
get_theta()
))
theta_decimal.add_updater(lambda m: m.next_to(
self.pendulum.theta_label, DOWN
))
theta_decimal.add_updater(lambda m: m.set_color(
GREEN if get_theta() > 0 else RED
))
self.set_theta(0)
self.wait(2)
self.set_theta(89.9 * DEGREES, run_time=3)
self.wait(2)
self.set_theta(60 * DEGREES, run_time=2)
self.wait()
self.play(FadeInFrom(theta_decimal, UP))
self.set_theta(-60 * DEGREES, run_time=4)
self.set_theta(60 * DEGREES, run_time=4)
self.play(FadeOut(theta_decimal))
def show_angle_geometry(self):
g_vect = self.g_vect
vectors = VGroup(
g_vect, g_vect.tangent, g_vect.perp,
)
g_line = Line(
g_vect.get_start(),
g_vect.get_end(),
stroke_width=1,
stroke_color=WHITE,
)
arc = Arc(
start_angle=90 * DEGREES,
angle=self.pendulum.get_theta(),
radius=0.5,
arc_center=g_vect.get_end(),
)
q_mark = TexMobject("?")
q_mark.next_to(arc.get_center(), UL, SMALL_BUFF)
theta_label = TexMobject("\\theta")
theta_label.move_to(q_mark)
opposite = g_vect.component_lines[0].copy()
adjascent = g_line.copy()
opposite.set_stroke(BLUE, 5, opacity=1)
adjascent.set_stroke(YELLOW, 5)
vectors.save_state()
vectors.clear_updaters()
self.add(g_line, g_vect)
self.play(vectors.set_opacity, 0.3)
self.play(
ShowCreation(arc),
Write(q_mark)
)
self.play(ShowCreationThenFadeAround(q_mark))
self.wait()
self.play(ShowCreationThenFadeAround(
self.pendulum.theta_label
))
self.play(
TransformFromCopy(
self.pendulum.theta_label,
theta_label,
),
FadeOut(q_mark)
)
self.wait()
self.play(ShowCreation(opposite))
self.play(ShowCreation(adjascent))
self.wait()
self.play(
FadeOut(opposite),
FadeOut(adjascent),
)
self.play(
Restore(vectors),
FadeOut(arc),
FadeOut(theta_label),
)
# vectors.resume_updating()
def ask_about_what_to_do(self):
pass
g_vect = self.g_vect
g_sin_label = self.g_sin_label
angle = g_vect.tangent.get_angle()
angle = (angle - PI) % TAU
randy = You()
randy.to_corner(DL)
bubble = randy.get_bubble(
height=2,
width=2,
)
thought_term = g_sin_label.copy()
thought_term.rotate(-angle)
thought_term.move_to(bubble.get_bubble_center())
rect = SurroundingRectangle(thought_term)
rect.rotate(angle)
rect.move_to(g_sin_label)
randy.save_state()
randy.fade(1)
self.play(randy.restore, randy.change, "pondering")
self.play(ShowCreationThenFadeOut(rect))
self.play(
ShowCreation(bubble),
TransformFromCopy(g_sin_label, thought_term),
randy.look_at, bubble,
)
self.play(Blink(randy))
self.wait()
thought_term.remove(thought_term[0])
self.play(
ShowCreationThenDestruction(
thought_term.copy().set_style(
stroke_color=YELLOW,
stroke_width=2,
fill_opacity=0,
),
run_time=2
)
)
self.play(
randy.change, "confused", thought_term,
)
self.play(Blink(randy))
#
def set_theta(self, value, *added_anims, **kwargs):
kwargs["run_time"] = kwargs.get("run_time", 2)
self.play(
self.theta_tracker.set_value, value,
*added_anims,
**kwargs,
)
class BuildUpEquation(Scene):
def construct(self):
self.show_velocity_and_position()
self.show_derivatives()
self.show_equation()
self.talk_about_sine_component()
self.add_air_resistance()
def show_velocity_and_position(self):
pass