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.
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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Topic Video
Question
please answer part c only. there are no external forces. and show work
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.
Transcribed Image Text:2
COordin
O =
egn ol
wconstraint-
d0. 元=d&
dt
ア= 1
2.
レニ0
(No externel Force)
2.
L.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
