A chain of length L, mass M lies on a frictionless table with a part of length z hanging through a small hole. a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show details). b) Write down the Euler-Lagrange equation for the coordinate z.
A chain of length L, mass M lies on a frictionless table with a part of length z hanging through a small hole. a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show details). b) Write down the Euler-Lagrange equation for the coordinate z.
Classical Dynamics of Particles and Systems
5th Edition
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Stephen T. Thornton, Jerry B. Marion
Chapter7: Hamilton's Principle-lagrangian And Hamiltonian Dynamics
Section: Chapter Questions
Problem 7.1P
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![A chain of length L, mass M lies on a frictionless table with a part of length z hanging
through a small hole.
a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show
details).
b) Write down the Euler-Lagrange equation for the coordinate z.
c) Find z(t) if the chain is released from rest with length zo initially hanging from the table.
d) How long after it is released from rest will the chain completely fall of the table?
Nu](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4fdacf83-4e41-472e-a742-4af5bc7df5a7%2F0c37a81b-fe3a-480b-b024-7fb55bee8fe4%2Fewhzi4h_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A chain of length L, mass M lies on a frictionless table with a part of length z hanging
through a small hole.
a) Use z as the generalized coordinate to write the Lagrangian of the system. (Show
details).
b) Write down the Euler-Lagrange equation for the coordinate z.
c) Find z(t) if the chain is released from rest with length zo initially hanging from the table.
d) How long after it is released from rest will the chain completely fall of the table?
Nu
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