exemple pendule à ressort
This commit is contained in:
Didictateur
parent
d2f533dce9
commit
6abe888da4
4 changed files with 249 additions and 62 deletions
58
chute_libre.py
Normal file
58
chute_libre.py
Normal file
|
|
@ -0,0 +1,58 @@
|
|||
import legrandchien as lgc
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib.animation as animation
|
||||
|
||||
g = lgc.Const(10)
|
||||
m = lgc.Const(1)
|
||||
|
||||
x = lgc.Var("x")
|
||||
y = lgc.Var("y")
|
||||
|
||||
T = 0.5 * m * (x.diff() * x.diff() + y.diff() * y.diff())
|
||||
V = m * g * y
|
||||
L = T - V
|
||||
|
||||
dico = {
|
||||
"x" : 0,
|
||||
"d_x" : 1,
|
||||
"y" : 0,
|
||||
"d_y" : 1
|
||||
}
|
||||
|
||||
values = L.solve(dico, 10, 0.1)
|
||||
|
||||
# Extraire les données pour x et y
|
||||
times = sorted(values.keys())
|
||||
positions_x = [values[t]["x"] for t in times]
|
||||
positions_y = [values[t]["y"] for t in times]
|
||||
|
||||
# Créer la figure
|
||||
fig, ax = plt.subplots(figsize=(8, 8))
|
||||
ax.set_xlim(min(positions_x) - 5, max(positions_x) + 5)
|
||||
ax.set_ylim(min(positions_y) - 5, max(positions_y) + 5)
|
||||
ax.set_xlabel("X (m)")
|
||||
ax.set_ylabel("Y (m)")
|
||||
ax.grid(True)
|
||||
|
||||
# Point animé
|
||||
point, = ax.plot([], [], 'ro', markersize=15, label="Particule")
|
||||
# Trajectoire
|
||||
line, = ax.plot([], [], 'b-', alpha=0.3, linewidth=2, label="Trajectoire")
|
||||
# Texte temps
|
||||
time_text = ax.text(0.02, 0.95, '', transform=ax.transAxes, fontsize=12)
|
||||
|
||||
ax.legend()
|
||||
|
||||
def animate(frame):
|
||||
# Point courant
|
||||
point.set_data([positions_x[frame]], [positions_y[frame]])
|
||||
# Trajectoire jusqu'au point courant
|
||||
line.set_data(positions_x[:frame + 1], positions_y[:frame + 1])
|
||||
# Texte
|
||||
time_text.set_text(f"t = {times[frame]:.2f}s\nx = {positions_x[frame]:.2f}m, y = {positions_y[frame]:.2f}m")
|
||||
return point, line, time_text
|
||||
|
||||
ani = animation.FuncAnimation(fig, animate, frames=len(times),
|
||||
interval=50, blit=True, repeat=True)
|
||||
|
||||
plt.show()
|
||||
59
example.py
59
example.py
|
|
@ -1,59 +0,0 @@
|
|||
import legrandchien as lgc
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib.animation as animation
|
||||
|
||||
if __name__ == "__main__":
|
||||
g = lgc.Const(10)
|
||||
m = lgc.Const(1)
|
||||
|
||||
x = lgc.Var("x")
|
||||
y = lgc.Var("y")
|
||||
|
||||
T = 0.5 * m * (x.diff() * x.diff() + y.diff() * y.diff())
|
||||
V = m * g * y
|
||||
L = T - V
|
||||
|
||||
dico = {
|
||||
"x" : 0,
|
||||
"d_x" : 1,
|
||||
"y" : 0,
|
||||
"d_y" : 1
|
||||
}
|
||||
|
||||
values = L.solve(dico, 10, 0.1)
|
||||
|
||||
# Extraire les données pour x et y
|
||||
times = sorted(values.keys())
|
||||
positions_x = [values[t]["x"] for t in times]
|
||||
positions_y = [values[t]["y"] for t in times]
|
||||
|
||||
# Créer la figure
|
||||
fig, ax = plt.subplots(figsize=(8, 8))
|
||||
ax.set_xlim(min(positions_x) - 5, max(positions_x) + 5)
|
||||
ax.set_ylim(min(positions_y) - 5, max(positions_y) + 5)
|
||||
ax.set_xlabel("X (m)")
|
||||
ax.set_ylabel("Y (m)")
|
||||
ax.grid(True)
|
||||
|
||||
# Point animé
|
||||
point, = ax.plot([], [], 'ro', markersize=15, label="Particule")
|
||||
# Trajectoire
|
||||
line, = ax.plot([], [], 'b-', alpha=0.3, linewidth=2, label="Trajectoire")
|
||||
# Texte temps
|
||||
time_text = ax.text(0.02, 0.95, '', transform=ax.transAxes, fontsize=12)
|
||||
|
||||
ax.legend()
|
||||
|
||||
def animate(frame):
|
||||
# Point courant
|
||||
point.set_data([positions_x[frame]], [positions_y[frame]])
|
||||
# Trajectoire jusqu'au point courant
|
||||
line.set_data(positions_x[:frame + 1], positions_y[:frame + 1])
|
||||
# Texte
|
||||
time_text.set_text(f"t = {times[frame]:.2f}s\nx = {positions_x[frame]:.2f}m, y = {positions_y[frame]:.2f}m")
|
||||
return point, line, time_text
|
||||
|
||||
ani = animation.FuncAnimation(fig, animate, frames=len(times),
|
||||
interval=50, blit=True, repeat=True)
|
||||
|
||||
plt.show()
|
||||
138
legrandchien.py
138
legrandchien.py
|
|
@ -1,5 +1,6 @@
|
|||
from enum import Enum
|
||||
import numpy as np
|
||||
from tqdm import tqdm
|
||||
|
||||
class Operation(Enum):
|
||||
VAR = 1
|
||||
|
|
@ -363,6 +364,8 @@ class Equation:
|
|||
return Equation(Operation.CONST, None, None, Const(self.value.value))
|
||||
if self.op == Operation.VAR:
|
||||
return Equation(Operation.VAR, None, None, Var(self.value.name, self.value.degree))
|
||||
if self.op in {Operation.SIN, Operation.COS}:
|
||||
return Equation(self.op, None, None, self.value.copy())
|
||||
return Equation(self.op, self.left.copy(), self.right.copy(), None)
|
||||
|
||||
def diff(self):
|
||||
|
|
@ -379,6 +382,10 @@ class Equation:
|
|||
if self.op == Operation.DIV:
|
||||
return (self.left.diff()*self.right.copy() - self.left.copy()*self.right.diff()) \
|
||||
/ (self.right.copy()*self.right.copy())
|
||||
if self.op == Operation.SIN:
|
||||
return self.value.diff() * Equation(Operation.COS, None, None, self.value.copy())
|
||||
if self.op == Operation.COS:
|
||||
return Const(-1) * self.value.diff() * Equation(Operation.SIN, None, None, self.value.copy())
|
||||
|
||||
def partial(self, var_name):
|
||||
if self.op == Operation.CONST:
|
||||
|
|
@ -397,6 +404,10 @@ class Equation:
|
|||
if self.op == Operation.DIV:
|
||||
return (self.left.partial(var_name)*self.right.copy() - self.left.copy()*self.right.partial(var_name)) \
|
||||
/ (self.right.copy()*self.right.copy())
|
||||
if self.op == Operation.SIN:
|
||||
return self.value.partial(var_name) * Equation(Operation.COS, None, None, self.value.copy())
|
||||
if self.op == Operation.COS:
|
||||
return Const(-1) * self.value.partial(var_name) * Equation(Operation.SIN, None, None, self.value.copy())
|
||||
|
||||
def evaluate(self, dico):
|
||||
if self.op == Operation.CONST:
|
||||
|
|
@ -411,17 +422,23 @@ class Equation:
|
|||
return self.left.evaluate(dico) * self.right.evaluate(dico)
|
||||
if self.op == Operation.DIV:
|
||||
return self.left.evaluate(dico) / self.right.evaluate(dico)
|
||||
if self.op == Operation.SIN:
|
||||
return np.sin(self.value.evaluate(dico))
|
||||
if self.op == Operation.COS:
|
||||
return np.cos(self.value.evaluate(dico))
|
||||
|
||||
def solve(self, dico, tmax=10, dt=0.01):
|
||||
self.simplify()
|
||||
variables = self.getAllVar()
|
||||
|
||||
equations = []
|
||||
print([v.name for v in variables])
|
||||
# print([v.name for v in variables])
|
||||
for var in variables:
|
||||
equations.append(self.partial(var.diff().name).diff() - self.partial(var.name))
|
||||
|
||||
unknown = self.getUnknown(dico)
|
||||
for eq in equations:
|
||||
eq.simplify()
|
||||
unknown = unknown.union(eq.getUnknown(dico))
|
||||
|
||||
t = 0
|
||||
|
|
@ -430,6 +447,8 @@ class Equation:
|
|||
for var in unknown:
|
||||
dico[var.name] = 0.
|
||||
|
||||
# print([var.name for var in unknown])
|
||||
# print(equations[0])
|
||||
assert(len(unknown) == len(equations))
|
||||
n = len(unknown)
|
||||
|
||||
|
|
@ -437,9 +456,13 @@ class Equation:
|
|||
unknown = list(unknown)
|
||||
equations = list(equations)
|
||||
|
||||
while t <= tmax:
|
||||
for t in tqdm([n * dt for n in range(int(tmax/dt))]):
|
||||
err = 1
|
||||
while err > 10**-6:
|
||||
iterations = 0
|
||||
max_iteration = 50
|
||||
|
||||
while err > 10**-6 and iterations < max_iteration:
|
||||
iterations += 1
|
||||
# jacobian
|
||||
J = np.zeros((n, n))
|
||||
F = np.zeros(n)
|
||||
|
|
@ -483,17 +506,102 @@ class Equation:
|
|||
return {self.value.copy()}
|
||||
else:
|
||||
return {Var(self.value.name[2*self.value.degree:], 0)}
|
||||
if self.op in {Operation.SIN, Operation.COS}:
|
||||
return self.value.getAllVar()
|
||||
return self.left.getAllVar().union(self.right.getAllVar())
|
||||
|
||||
def getUnknown(self, dico):
|
||||
# print(self)
|
||||
if self.op == Operation.CONST:
|
||||
return set()
|
||||
if self.op == Operation.VAR:
|
||||
if self.value.name not in dico:
|
||||
return {self.value}
|
||||
return set()
|
||||
if self.op in {Operation.SIN, Operation.COS}:
|
||||
return self.value.getUnknown(dico)
|
||||
return self.left.getUnknown(dico).union(self.right.getUnknown(dico))
|
||||
|
||||
def simplify(self):
|
||||
if self.left != None:
|
||||
self.left.simplify()
|
||||
if self.right != None:
|
||||
self.right.simplify()
|
||||
if self.op in {Operation.SIN, Operation.COS}:
|
||||
self.value.simplify()
|
||||
|
||||
if self.op == Operation.CONST:
|
||||
pass
|
||||
if self.op == Operation.VAR:
|
||||
pass
|
||||
|
||||
if self.op == Operation.ADD:
|
||||
if self.left.op == Operation.CONST and self.right.op == Operation.CONST:
|
||||
self.op = Operation.CONST
|
||||
self.value = Const(self.left.value.value + self.right.value.value)
|
||||
self.left = None
|
||||
self.right = None
|
||||
elif self.left.op == Operation.CONST and self.left.value.value == 0:
|
||||
self.op = self.right.op
|
||||
self.left = self.right.left
|
||||
self.value = self.right.value
|
||||
self.right = self.right.right
|
||||
elif self.right.op == Operation.CONST and self.right.value.value == 0:
|
||||
self.op = self.left.op
|
||||
self.right = self.left.right
|
||||
self.value = self.left.value
|
||||
self.left = self.left.left
|
||||
|
||||
if self.op == Operation.SUB:
|
||||
if self.left.op == Operation.CONST and self.right.op == Operation.CONST:
|
||||
self.op = Operation.CONST
|
||||
self.value = Const(self.left.value.value - self.right.value.value)
|
||||
self.left = None
|
||||
self.right = None
|
||||
elif self.right.op == Operation.CONST and self.right.value.value == 0:
|
||||
self = self.left
|
||||
|
||||
if self.op == Operation.MULT:
|
||||
if self.left.op == Operation.CONST and self.right.op == Operation.CONST:
|
||||
self.op = Operation.CONST
|
||||
self.value = Const(self.left.value.value * self.right.value.value)
|
||||
self.left = None
|
||||
self.right = None
|
||||
elif self.left.op == Operation.CONST and self.left.value.value == 0:
|
||||
self.op = Operation.CONST
|
||||
self.left = None
|
||||
self.right = None
|
||||
self.value = Const(0)
|
||||
elif self.right.op == Operation.CONST and self.right.value.value == 0:
|
||||
self.op = Operation.CONST
|
||||
self.left = None
|
||||
self.right = None
|
||||
self.value = Const(0)
|
||||
elif self.left.op == Operation.CONST and self.left.value.value == 1:
|
||||
self.op = self.right.op
|
||||
self.left = self.right.left
|
||||
self.value = self.right.value
|
||||
self.right = self.right.right
|
||||
elif self.right.op == Operation.CONST and self.right.value.value == 1:
|
||||
self.op = self.left.op
|
||||
self.right = self.left.right
|
||||
self.value = self.left.value
|
||||
self.left = self.left.left
|
||||
|
||||
if self.op == Operation.SIN:
|
||||
if self.value.op == Operation.CONST:
|
||||
self.op = Operation.CONST
|
||||
self.left = None
|
||||
self.right = None
|
||||
self.value = Const(np.sin(self.value.value))
|
||||
|
||||
if self.op == Operation.COS:
|
||||
if self.value.op == Operation.CONST:
|
||||
self.op = Operation.CONST
|
||||
self.left = None
|
||||
self.right = None
|
||||
self.value = Const(np.cos(self.value.value))
|
||||
|
||||
def __str__(self):
|
||||
if self.op == Operation.CONST:
|
||||
return str(self.value.value)
|
||||
|
|
@ -507,6 +615,10 @@ class Equation:
|
|||
return f"({str(self.left)})*({str(self.right)})"
|
||||
if self.op == Operation.DIV:
|
||||
return f"({str(self.left)})/({str(self.right)})"
|
||||
if self.op == Operation.SIN:
|
||||
return f"sin({str(self.value)})"
|
||||
if self.op == Operation.COS:
|
||||
return f"cos({str(self.value)})"
|
||||
|
||||
def __add__(self, other):
|
||||
if other.type == "Const":
|
||||
|
|
@ -595,3 +707,23 @@ class Equation:
|
|||
def __rtruediv__(self, other):
|
||||
if isinstance(other, (int, float)):
|
||||
return Const(other) / self
|
||||
|
||||
def cos(value):
|
||||
if isinstance(value, (float, int)):
|
||||
return Equation(Operation.CONST, None, None, np.cos(value))
|
||||
if value.type == "Const":
|
||||
return Equation(Operation.CONST, None, None, np.cos(value.value))
|
||||
if value.type == "Var":
|
||||
return Equation(Operation.COS, None, None, Equation(Operation.VAR, None, None, value.copy()))
|
||||
if value.type == "Equation":
|
||||
return Equation(Operation.COS, None, None, value.copy())
|
||||
|
||||
def sin(value):
|
||||
if isinstance(value, (float, int)):
|
||||
return Equation(Operation.CONST, None, None, np.sin(value))
|
||||
if value.type == "Const":
|
||||
return Equation(Operation.CONST, None, None, np.sin(value.value))
|
||||
if value.type == "Var":
|
||||
return Equation(Operation.SIN, None, None, Equation(Operation.VAR, None, None, value.copy()))
|
||||
if value.type == "Equation":
|
||||
return Equation(Operation.SIN, None, None, value.copy())
|
||||
56
pendule_a_ressort.py
Normal file
56
pendule_a_ressort.py
Normal file
|
|
@ -0,0 +1,56 @@
|
|||
import legrandchien as lgc
|
||||
import matplotlib.pyplot as plt
|
||||
import matplotlib.animation as animation
|
||||
import numpy as np
|
||||
|
||||
g = lgc.Const(10)
|
||||
m = lgc.Const(1)
|
||||
k = lgc.Const(10)
|
||||
r0 = lgc.Const(1)
|
||||
|
||||
theta = lgc.Var("theta")
|
||||
r = lgc.Var("r")
|
||||
|
||||
x = r * lgc.cos(theta)
|
||||
y = r * lgc.sin(theta)
|
||||
|
||||
T = 0.5 * m * (x.diff()*x.diff() + y.diff()*y.diff())
|
||||
V = m * g * r * lgc.cos(theta) + k * (r - r0) * (r - r0)
|
||||
|
||||
L = T - V
|
||||
|
||||
dico = {
|
||||
"theta" : -3.14/2,
|
||||
"d_theta" : 0,
|
||||
"r" : 1.2,
|
||||
"d_r" : 0,
|
||||
}
|
||||
|
||||
data = L.solve(dico, 10, 0.01)
|
||||
|
||||
# Extraire les positions
|
||||
times = sorted(data.keys())
|
||||
positions = [data[t] for t in times]
|
||||
|
||||
x_positions = [p["r"] * np.sin(p["theta"]) for p in positions]
|
||||
y_positions = [p["r"] * np.cos(p["theta"]) for p in positions]
|
||||
|
||||
# Créer la figure et l'axe
|
||||
fig, ax = plt.subplots(figsize=(8, 8))
|
||||
ax.set_xlim(-3, 3)
|
||||
ax.set_ylim(-3, 3)
|
||||
ax.set_xlabel("X (m)")
|
||||
ax.set_ylabel("Y (m)")
|
||||
ax.grid(True)
|
||||
|
||||
line, = ax.plot([], [], 'o-', lw=2, markersize=8)
|
||||
trace, = ax.plot([], [], 'r-', alpha=0.3, lw=1)
|
||||
|
||||
def animate(frame):
|
||||
line.set_data([0, x_positions[frame]], [0, y_positions[frame]])
|
||||
trace.set_data(x_positions[:frame+1], y_positions[:frame+1])
|
||||
return line, trace
|
||||
|
||||
anim = animation.FuncAnimation(fig, animate, frames=len(x_positions), interval=50, blit=True, repeat=True)
|
||||
|
||||
plt.show()
|
||||
Loading…
Reference in a new issue