A question about Analytical Mechanics

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Homework Help Overview

The discussion revolves around concepts in Analytical Mechanics, specifically focusing on the nature of generalized coordinates and their variations compared to Cartesian coordinates. Participants are exploring the implications of setting variations to zero and how this relates to the formulation of Lagrange's equations.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the conditions under which variations in generalized coordinates can be zero, contrasting this with the necessity for variations in Cartesian coordinates to be non-zero. There is a request for concrete explanations regarding these differences.

Discussion Status

The discussion is active, with participants seeking clarification on the theoretical underpinnings of variations in coordinates. Some guidance has been offered regarding the role of generalized coordinates in Lagrange's equations, but no consensus has been reached on the specific reasons for the differences in treatment of δq and δx.

Contextual Notes

Participants are navigating the complexities of Analytical Mechanics, and there may be assumptions about the definitions and roles of generalized coordinates that are not fully articulated. The reference to Weinstock's book suggests a resource for deeper exploration of the topic.

enricfemi
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i am studing Analytical Mechanics in these days.it is really amazing. but a question pazzles me .it seems:

to generalized coordinates q,δq is arbitrary,it can equal 0;while variation in the x-coordinate, δx is not.

i just cann't understand
 
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In variation, delta x cannot be zero because you eventually divide by it.
 
could you concretely explain why delta q can be zero.

thank you very much!
 
i think when x is changed ,q should be also change.

help ,help ,can anybody help me?
 
It depends on what your generalized coordinates are.

The derivation with variations like [tex]\delta q_i[/tex] depends on the variation possibly being anything at all. Lagrange's equations arise from the fact that you have a product of two functions in an integral that equals zero. Since the variation in the generalized coordinates could, in general, be anything, the other function has to be uniformly zero. Weinstock's book in Dover edition covers this point quite nicely.
 

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