Lagrangian Mechanics

In this repo I'll add all my projects involving Lagrangian Mechanics to solve complex dynamic systems.

This formulation of classical mechanics is based on the principle of least action or Hamilton's principle, it simply states that a system chooses a path where the action is minimized, this principle is formalized the following way:

$$ \delta S=0,\quad\mathrm{where}\quad S=\int_{t_1}^{t_2}L(q,\dot{q},t)dt $$

The "recipe" to get a function $L$ that minimizes the action is the Euler-Lagrange Equation

$$ \frac{d}{dt}\left(\frac{\partial L}{\partial\dot{q}}\right)-\frac{\partial L}{\partial q}=0 $$

where

• $L = T - V$ is the functional, called Lagrangian
• $q$ is the generalized coordinate
• $\dot{q}$ is the generalized velocity