Lagrange Equations-Classical and Relativistic Mechanics-Lecture Handout, Exercises of Classical and Relativistic Mechanics

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D’Alembert’s Principle and

Lagrange Equations

• Use principle of virtual work to derive
• Lagrange equations for systems with

holonomic constraints

Don’t ever give up!

Physics Student

PhD Program

Double Pendulum: General

Coordinates

Constrained motion

Bead slides without friction on a vertical circular loop, in a uniform

Gravitational field. Hoop rotates at a constant angular velocity.

Velocity dependent potentials: if

forces derived from U via

Charged particle in electromagnetic

field

• Lorentz force

F=q[E+(v x B)]

U  q   qA. v

Atwood’s Machine

V= -M1g x – M2 g(l-x)

Bead sliding on rotating straight

wire, g=

Problem to think about