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.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
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please answer part c only. there are no external forces. and show work 

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.
2
COordin
O =
egn ol
wconstraint-
d0. 元=d&
dt
ア= 1
2.
レニ0
(No externel Force)
2.
L.
Transcribed Image Text:2 COordin O = egn ol wconstraint- d0. 元=d& dt ア= 1 2. レニ0 (No externel Force) 2. L.
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