PROBLEMS 1.1 For each of the following systems, specify the number of degrees of freedom and a set of good coordinates. (a) A bead constrained to move on a closed circular hoop that is fixed in space. (b) A bead constrained to move on a helix of constant pitch and constant radius. (c) A particle on a right circular cylinder. (d) A pair of scissors on a plane. (e) A rigid rod in 3-space. (f) A rigid cross in 3-space. (g) A linear spring in 3-space. (h) Any rigid body with one point fixed. (i) A hydrogen atom. (j) A lithium atom. (k) A compound pendulum (two pendulums attached end to end). 1.2 Show that a particle constrained to move on a curve of any shape has one degree of freedom.

PROBLEMS 1.1 For each of the following systems, specify the number of degrees of freedom and a set of good coordinates. (a) A bead constrained to move on a closed circular hoop that is fixed in space. (b) A bead constrained to move on a helix of constant pitch and constant radius. (c) A particle on a right circular cylinder. (d) A pair of scissors on a plane. (e) A rigid rod in 3-space. (f) A rigid cross in 3-space. (g) A linear spring in 3-space. (h) Any rigid body with one point fixed. (i) A hydrogen atom. (j) A lithium atom. (k) A compound pendulum (two pendulums attached end to end). 1.2 Show that a particle constrained to move on a curve of any shape has one degree of freedom.

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 7.32P

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