Virtual Displacement: Analyzing Langrange Equations

  • Context: Graduate 
  • Thread starter Thread starter wormhole
  • Start date Start date
  • Tags Tags
    Displacement Virtual
Click For Summary
SUMMARY

The discussion focuses on the concept of virtual displacement in the context of Lagrange equations within analytical mechanics. Virtual displacement is defined as a small change in the position of a particle that adheres to constraints without the passage of time and without altering unknown forces. Participants express confusion regarding the definition's assertion of "no time passing" and the differentiation process that only considers generalized coordinates (q), excluding time. Clarification on these points is essential for a comprehensive understanding of Lagrangian mechanics.

PREREQUISITES
  • Understanding of Lagrange equations in analytical mechanics
  • Familiarity with generalized coordinates (q)
  • Basic knowledge of calculus, particularly differentiation
  • Concept of constraints in mechanical systems
NEXT STEPS
  • Study the derivation and application of Lagrange's equations in analytical mechanics
  • Explore the concept of generalized coordinates and their significance in mechanics
  • Learn about the role of constraints in virtual work and displacement
  • Investigate the mathematical foundations of differentiation in the context of physics
USEFUL FOR

Students of analytical mechanics, physics enthusiasts, and educators seeking to deepen their understanding of Lagrange equations and virtual displacements in mechanical systems.

wormhole
Messages
28
Reaction score
0
hey, all

i'm now studiynd analytical mechanics and the subject is Langrange equations. What i can't grasp is the meaning of virtual displacement term.

The formal definition says that:
it's a small displacement of particle with agreement to constraints in such a way that no time passes and uknown forces don't change. The displacement itself has no relation to actual particle path.

there are two places where i get confused:

1) the definition itself when it says that "no time passes"

2) the actual calculation of virtual displacement where i don't understand the reason why the differentiation is done only with respect to generalized coordinates (q) and time is ignored...

Xj - cartezian coordinates
delta(Xj) - virtual displacement of Xj
Qk - generalized coordinates

formula.jpg
 
Last edited:
Physics news on Phys.org
Look at your identical post in www.advancedphysics.org[/URL]
 
Last edited by a moderator:

Similar threads

Undergrad Virtual displacement is not consistent with constraints
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Virtual work and constraint forces
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Prerequisites needed to grasp virtual displacement
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Virtual displacements and Virtual Work
  • · Replies 4 ·
Replies
4
Views
14K
Graduate Virtual work and kinetic energy
  • · Replies 17 ·
Replies
17
Views
5K
Graduate Hamilton's Principle and the Principle of Virtual Work
  • · Replies 1 ·
Replies
1
Views
5K
Graduate Static Equilibrium and D'Alembert's Principle
  • · Replies 2 ·
Replies
2
Views
3K
Graduate Equation of motion of a marble moving on a generic vertical guide
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Drag equation - relative flow velocity
  • · Replies 11 ·
Replies
11
Views
4K
Graduate Weyl tensor and coordinate acceleration
  • · Replies 12 ·
Replies
12
Views
3K