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

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

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 final exam Due date: Thursday, May 13 15. Particle on a helix 9 points A particle of mass m moves under the influence 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
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern