Question 4A particle of mass m moves in a central force field with potential V(r). The La-grangian in terms of spherical polar coordinates (r,0,¢) is1L = ;m (² +r²e² + ² sin² 0¢? ) – V(r).1. Find the momenta (pr, pe, pp) conjugate to (r,0,4).2. Find the Hamiltonian H(r,0,4,,pr, Po, Pp).3. Write down the explicit Hamiltonian's equations of motion.?Answer.

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A particle of mass m moves in a central force field with potential V(r). The La- grangian in terms of spherical polar coordinates (r, 0, 4) is m (2 +rô² +r² sin² 04? ) – V(r). 1. Find the momenta (p, Po, Po) conjugate to (r,0,p). 2. Find the Hamiltonian H(r,0,4,,Pr, Pe, Pg). 3. Write down the explicit Hamiltonian's equations of motion. ?

A particle of mass m moves in a central force field with potential V(r). The La- grangian in terms of spherical polar coordinates (r, 0, 4) is m (2 +rô² +r² sin² 04? ) – V(r). 1. Find the momenta (p, Po, Po) conjugate to (r,0,p). 2. Find the Hamiltonian H(r,0,4,,Pr, Pe, Pg). 3. Write down the explicit Hamiltonian's equations of motion. ?

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics

Section: Chapter Questions

Problem 7.25P

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