A bead of mass m slides on a long straight wire which makes an angle a with the upward vertical and rotates with constant angular velocity o = w. Gravity g works vertically downwards. After choosing appropriate generalized coordinates, the Lagrangian is, m

A bead of mass m slides on a long straight wire which makes an angle a with the upward vertical and rotates with constant angular velocity o = w. Gravity g works vertically downwards. After choosing appropriate generalized coordinates, the Lagrangian is, m

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 7.5P

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Concept explainers

Rigid Body

A rigid body is an object which does not change its shape or undergo any significant deformation due to an external force or movement. Mathematically speaking, the distance between any two points inside the body doesn't change in any situation.

Rigid Body Dynamics

Rigid bodies are defined as inelastic shapes with negligible deformation, giving them an unchanging center of mass. It is also generally assumed that the mass of a rigid body is uniformly distributed. This property of rigid bodies comes in handy when we deal with concepts like momentum, angular momentum, force and torque. The study of these properties – viz., force, torque, momentum, and angular momentum – of a rigid body, is collectively known as rigid body dynamics (RBD).

Question

A bead of mass m slides on a long straight wire which makes an angle a with the upward vertical and rotates with constant
angular velocity o = w. Gravity g works vertically downwards. After choosing appropriate generalized coordinates, the
Lagrangian is,
m

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