set6 - Department of Physics The Ohio State University Prof...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Department of Physics Prof. R. Bundschuh The Ohio State University Sixth Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: May 11 9:30am-10:18am midterm exam, May 31 no class, Jun 9 9:30am-11:18am Fnal exam Due date: Thursday, May 13 15. Particle on a helix 9 points A particle of mass m moves under the in±uence of gravity along the helix z = , r = constant, where k is a constant and the z -axis points vertically upwards. a) Write down the Lagrangian of the system expressing it in the variable z . b) Calculate the generalized momentum p z . c) Calculate the Hamiltonian in terms of the variables z and p z . d) Derive the Hamiltonian equations of motion of the system. e) Solve the Hamiltonian equations of motion. 16. Hamiltonians and energy 22 points In this problem we want to develop a feeling for the relationship between the Hamiltonian and the total energy of a system and their conservation. To this end, write down the kinetic energy, the potential energy, the total energy, the Lagrangian, the generalized momenta, and
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 07/17/2008 for the course PHYS 664 taught by Professor Bundschuh during the Fall '04 term at Ohio State.

Ask a homework question - tutors are online