pysicm

The goal of this project is to work through the Structure and Interpretation of Classical Mechanics book using Python and the sympy library.

Each chapter of the book will have a notebook dedicated in the notebooks folder.

So far I have only completed the first section.

1.4 Computing Actions

from sympy import symbols, Rational, integrate, Function
from sympy import Matrix

x = Function('x')
y = Function('y')
z = Function('z')
t = symbols('t')
m = symbols('m')

q = Matrix([x(t), y(t), z(t)])

def velocity(local):
    return Matrix(local[4:7])


def l_free_particle(mass):
    def inner(local):
        v = velocity(local)
        return Rational(1,2) * mass * (v.transpose() * v)[0]
    
    return inner


def gamma(q, t):
    # Returns the local tuple
    return Matrix([t, q, q.diff()])


def lagrangian_action(L, q, t1, t2):
    return integrate(L(gamma(q,t)), (t, t1, t2))

test_path = Matrix([4 * t + 7, 3 * t + 5, 2 * t + 1])
test_path

$\displaystyle \left[\begin{matrix}4 t + 7\3 t + 5\2 t + 1\end{matrix}\right]$

l_free_particle(3.0)(gamma(q,t))

$\displaystyle 1.5 \left(\frac{d}{d t} x{\left(t \right)}\right)^{2} + 1.5 \left(\frac{d}{d t} y{\left(t \right)}\right)^{2} + 1.5 \left(\frac{d}{d t} z{\left(t \right)}\right)^{2}$

lagrangian_action(l_free_particle(3.0), test_path, 0.0, 10.0)

$\displaystyle 435.0$