Generalized Momentum

We have P=mv. We want to generalize it using Lagrangian and Hamiltonian. Why we choose Generalized coordinates and Lagrangian and Hamiltonian approaches is discussed in detail in this blog post.

For langrangian we have,
L=T—V

Put the value of kinetic energy interns of velocity and rate of change of displacement.

 

Differentiate the lagrangian w.r.t dx/dt or x dot. 



The expression becomes Pi.

We can replace xi with any generalized coordinates. 

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