A bead of mass m slides without friction on a straight wire. The wire rotates with constant velocity w around the origin in the x-y plane as shown in the figure to the right. The distance from the origin to the bead is r(t). There are no external forces. m r(1) e = wt (a) Determine the Lagrangian for this bead and its equation of constraint. (b) Eliminate the constraint and determine the Lagrange's equations of motion for the bead. (c) Write the Lagrange's equation with undetermined multipliers and determine the constraint force.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter4: Numerical Analysis Of Heat Conduction
Section: Chapter Questions
Problem 4.41P
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please answer only part c from this question

A bead of mass m slides without friction on a straight wire. The wire
rotates with constant velocity w around the origin in the x-y plane as
shown in the figure to the right. The distance from the origin to the
bead is r(t). There are no external forces.
m
r(1)
8 = wt
(a) Determine the Lagrangian for this bead and its equation of
constraint.
(b) Eliminate the constraint and determine the Lagrange's equations of motion for the
bead.
(c) Write the Lagrange's equation with undetermined multipliers and determine the
constraint force.
Transcribed Image Text:A bead of mass m slides without friction on a straight wire. The wire rotates with constant velocity w around the origin in the x-y plane as shown in the figure to the right. The distance from the origin to the bead is r(t). There are no external forces. m r(1) 8 = wt (a) Determine the Lagrangian for this bead and its equation of constraint. (b) Eliminate the constraint and determine the Lagrange's equations of motion for the bead. (c) Write the Lagrange's equation with undetermined multipliers and determine the constraint force.
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