Classical Mechanics 420

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Transcript Classical Mechanics 420

Classical Mechanics 420
J. D. Gunton
Lewis Lab 418
[email protected]
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
Homework Set 1 Number 2
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.
Vertical Disk Rolling On Plane
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
Polar Coordinates
Atwood’s Machine
V= -M1g x – M2 g(l-x)
Bead sliding on rotating straight
wire, g=0
Constrained motion
Bead slides without friction on a vertical circular loop, in a uniform
Gravitational field. Hoop rotates at a constant angular velocity.
Problem to think about