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introduction of lagrange equation

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What is the difference between Lagrange's equation of motion and Euler-Lagrange's equation of motion?

Both are same..just the names are different.


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In classical physics, Lagrange and Hamiltonian mechanics are two equivalent formulations used to describe the motion of particles or systems. Both approaches are based on the principle of least action, but they use different mathematical formalisms. Lagrange mechanics uses generalized coordinates and velocities to derive equations of motion, while Hamiltonian mechanics uses generalized coordinates and momenta. Despite their differences, Lagrange and Hamiltonian mechanics are related through a mathematical transformation called the Legendre transformation, which allows one to derive the equations of motion in either formalism from the other.


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