A question about Analytical Mechanics

Click For Summary
SUMMARY

The discussion focuses on the concept of generalized coordinates in Analytical Mechanics, specifically addressing the variations of these coordinates. It is established that while the variation in generalized coordinates (δq) can be arbitrary and equal to zero, the variation in Cartesian coordinates (δx) cannot be zero due to the necessity of division by this value in calculations. The derivation of Lagrange's equations is highlighted as being dependent on the variations of these coordinates, with Weinstock's book providing a comprehensive explanation of these principles.

PREREQUISITES
  • Understanding of Analytical Mechanics principles
  • Familiarity with generalized coordinates and their applications
  • Basic knowledge of Lagrange's equations
  • Experience with calculus, particularly in the context of variations
NEXT STEPS
  • Study Weinstock's book on Analytical Mechanics for deeper insights
  • Explore the derivation of Lagrange's equations in detail
  • Learn about the implications of variations in generalized coordinates
  • Investigate the relationship between generalized and Cartesian coordinates
USEFUL FOR

Students and professionals in physics, particularly those studying Analytical Mechanics, as well as educators seeking to clarify the concepts of generalized coordinates and their variations.

enricfemi
Messages
195
Reaction score
0
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
 
Physics news on Phys.org
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 \delta q_i 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.
 

Similar threads

  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
4
Views
722
  • · Replies 22 ·
Replies
22
Views
2K
  • · Replies 23 ·
Replies
23
Views
6K
  • · Replies 7 ·
Replies
7
Views
15K
  • · Replies 33 ·
2
Replies
33
Views
7K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 5 ·
Replies
5
Views
1K