Q.1) A particle of mass m moves in a central force field with pot ential V(r). The Lagrangian in terms of spherical polar coordinat es (r, 0, ø) is žm (* + r®* + r°sin° 0¿?) - v(r). 1 (2 + r²ở² + r² sin² 0ở3) – V (r). 1. Find the momenta (pr, Po, Po) conjugat e to (r, 0, ø). 2. Find the Hamiltonian H(r,0,¢, Pr, Po, Po). 3. Write down the explicit Hamilton's equation of motion.
Q.1) A particle of mass m moves in a central force field with pot ential V(r). The Lagrangian in terms of spherical polar coordinat es (r, 0, ø) is žm (* + r®* + r°sin° 0¿?) - v(r). 1 (2 + r²ở² + r² sin² 0ở3) – V (r). 1. Find the momenta (pr, Po, Po) conjugat e to (r, 0, ø). 2. Find the Hamiltonian H(r,0,¢, Pr, Po, Po). 3. Write down the explicit Hamilton's equation of motion.
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Transcribed Image Text:Q.1) A particle of mass m moves in a central force field with pot ential V(r). The Lagrangian
in terms of spherical polar coordinat es (r, 0, ¢) is
L = m (r² + r*ô° + r² sin? 0ộ³) – V (r).
2
1. Find the momenta (p,, po, Pó) conjugate to (r, 0, ø).
2. Find the Hamiltonian H(r, 0, ¢, Pr, Po, Pø).
3. Write down the explicit Hamilton's equation of motion.
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