- #1
tom777
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Hello guys!
Another question appeared during the preparation for my exam .
For some reason I don't feel 100% comfortable when dealing with
systems including pulleys and masses.
In the given exercise I'm supposed to calculate the kinetic energy T of the system
(which ultimately leads to the Lagrangian)
Scan of the problem:
http://img138.imageshack.us/img138/2064/question2.png [Broken]
The problem is solved by using methods of generalized coordinates
and Lagrangian functions.
So the thing is...I sort of know where most of the terms come from.
For example the (I_2/ (R_2)^2 ) probably comes from (d/dt y_{1} ) = (d/dt \theta_{2}) * R_1. However I'm lacking a concrete, rigorous approach to the problem.
What I mean by that is:
Say in cartesian coordinates the formula for the kinetic energy is given by:
T = 0.5 * m_1 * y_{mass 1} + 0.5 * m_2 * y_{mass 2}
How do I rigorously solve this problem now? I'm sort of puzzled - especially about
the last term in the equation for T in the scan. It seems as though some kind
of binomial formula might have been applied. But I'm not sure though.
I'd be really really happy if you could help me or give me a hint
on home to tackle these pulley-problems.
Thanks a lot in advance!
Another question appeared during the preparation for my exam .
For some reason I don't feel 100% comfortable when dealing with
systems including pulleys and masses.
In the given exercise I'm supposed to calculate the kinetic energy T of the system
(which ultimately leads to the Lagrangian)
Homework Statement
Scan of the problem:
http://img138.imageshack.us/img138/2064/question2.png [Broken]
Homework Equations
The problem is solved by using methods of generalized coordinates
and Lagrangian functions.
The Attempt at a Solution
So the thing is...I sort of know where most of the terms come from.
For example the (I_2/ (R_2)^2 ) probably comes from (d/dt y_{1} ) = (d/dt \theta_{2}) * R_1. However I'm lacking a concrete, rigorous approach to the problem.
What I mean by that is:
Say in cartesian coordinates the formula for the kinetic energy is given by:
T = 0.5 * m_1 * y_{mass 1} + 0.5 * m_2 * y_{mass 2}
How do I rigorously solve this problem now? I'm sort of puzzled - especially about
the last term in the equation for T in the scan. It seems as though some kind
of binomial formula might have been applied. But I'm not sure though.
I'd be really really happy if you could help me or give me a hint
on home to tackle these pulley-problems.
Thanks a lot in advance!
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