f. What is the Hamiltonian? g. Using Hamilton's equations of motion, determine the four equations of motion in terms of the conjugate momenta and coordinates. h. Does part g. agree with parts d. and e.? 3. Suppose that you have a particle of mass m subjected to gravity pointing downward that is constrained to move along the inside of a frictionless surface of a cone with angle a as shown below. Assume +z-axis is through center axis of cone pointing upward. а. Using spherical coordinates [x = r sin 0 cos o ,y =r sin 0 sin o, z = r cos 0], what is the equation of constraint? b. What is the kinetic energy expression of the particle after incorporating constraint? с. What is the potential energy expression of the particle after incorporating constraint? d. What are the resulting two equations of motion from Euler's equations and using answers in parts b. and c.? е. What are the conjugate momenta?

f. What is the Hamiltonian? g. Using Hamilton's equations of motion, determine the four equations of motion in terms of the conjugate momenta and coordinates. h. Does part g. agree with parts d. and e.? 3. Suppose that you have a particle of mass m subjected to gravity pointing downward that is constrained to move along the inside of a frictionless surface of a cone with angle a as shown below. Assume +z-axis is through center axis of cone pointing upward. а. Using spherical coordinates [x = r sin 0 cos o ,y =r sin 0 sin o, z = r cos 0], what is the equation of constraint? b. What is the kinetic energy expression of the particle after incorporating constraint? с. What is the potential energy expression of the particle after incorporating constraint? d. What are the resulting two equations of motion from Euler's equations and using answers in parts b. and c.? е. What are the conjugate momenta?

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter1: Introduction To Statics

Section: Chapter Questions

Problem 1.67P: For the position vectors P and Q shown, determine the orthogonal component of P Ă— Q in the...

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