# Hamiltonian mechanics Definition and 4 Discussions

Hamiltonian mechanics is a mathematically sophisticated formulation of classical mechanics. Historically, it contributed to the formulation of statistical mechanics and quantum mechanics. Hamiltonian mechanics was first formulated by William Rowan Hamilton in 1833, starting from Lagrangian mechanics, a previous reformulation of classical mechanics introduced by Joseph Louis Lagrange in 1788. Like Lagrangian mechanics, Hamiltonian mechanics is equivalent to Newton's laws of motion in the framework of classical mechanics.

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1. ### I Why can q(t) be something other than a spatial coordinate in the Euler-Lagrange equation?

Hello all, so I’ve been reading Jennifer Coopersmith’s The Lazy Universe: An Introduction to the Principle of Least Action, and on page 72 it says: If I understand it right, she’s saying that in our Euler-Lagrange equation ## \frac {\partial L} {\partial q} - \frac {d} {dt} \frac {\partial L}...
2. ### Other Math required for advanced classical mechanics

What types of math should a student be comfortable with going into a classical mechanics class at the level of Landau and Lifshitz? And are there any additional types of math that aren’t required, per se, but would be beneficial to know (for said course)?
3. ### Discrepancy in Lagrangian to Hamiltonian transformation?

I know, $$L=T-V \;\;\; \; \;\;\; [1]\;\;\; \; \;\;\; ( Lagrangian)$$ $$H=T+V \;\;\; \; \;\;\;[2] \;\;\; \; \;\;\; (Hamiltonian)$$ and logically, this leads to the equation,  H - L= 2V \;\;\; \; \;\;\...
4. ### I Generalized Momentum is a linear functional of Velocity?

Generalized momentum is covariant while velocity is contravariant in coordinate transformation on configuration space, thus they are defined in the tangent bundle and cotangent bundle respectively. Question: Is that means the momentum is a linear functional of velocity? If so, the way to...