- #1

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What about the Lagrange equation with the general force on the right hand side. I read in Goldstein that it can be, for instance, a non-conservative frictional force. Why? Where did that come from?

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- Thread starter Nikitin
- Start date

In summary, the conversation touches on the application of the Lagrange equation to holonomic constraints, the inclusion of constraining forces in the system, and the derivation of the Euler-Lagrange equation. It also raises questions about the modified equation and its application to different systems, as well as the relationship between kinetic energy and position. The answerer suggests referring to Goldstein's book for more clarification and also recommends a paper that discusses these topics.

- #1

- 735

- 27

What about the Lagrange equation with the general force on the right hand side. I read in Goldstein that it can be, for instance, a non-conservative frictional force. Why? Where did that come from?

- #2

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But what is up with the modified equation, ##\frac{\partial L }{\partial q_j} - \frac{d}{d t} \frac{\partial L }{\partial \dot{q_j}} = Q_j## ? When does this apply to a system, and for which generalized forces ##Q_j##s? It was not derived in Goldstein's book, just given.

- #3

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It might seem like a strange question because kinetic energy is defined using total velocity, but I ask because one form of Lagrange's equation is ##\frac{d}{dt} \frac{\partial T}{\partial \dot{q_j}} - \frac{\partial T}{\partial q_j} = Q_j##.

- #4

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Nikitin said:Another question, if somebody wants to answer: does ##\frac{\partial T}{\partial q_j}##, where ##T## is the kinetic energy of the system, always equal zero? Or do there exist situations where the kinetic energy has an explicit dependence on position?

It certainly can, in spherical coordinates (or polar) you have position dependence in the kinetic term.

- #5

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Check http://physics.clarku.edu/courses/201/sreading/AJP73_March2005_265-272.pdf [Broken] paper out. Does that help answer your questions?

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