Hamilton's principle and virtual work by constraint forces

Click For Summary
SUMMARY

The discussion centers on the interpretation of Hamilton's principle in relation to virtual work done by constraint forces, specifically in the context of holonomic and semiholonomic systems. Goldstein's assertion that the virtual work done by constraint forces is zero is based on the assumption of ideal constraints, which do not contribute to the right-hand side of equation (2.34). The conversation highlights a misunderstanding among some participants regarding D'Alembert's principle and the distinction between ideal and non-ideal constraints. The importance of foundational knowledge in classical mechanics is emphasized, particularly in relation to constraint forces.

PREREQUISITES
  • Understanding of Hamilton's principle
  • Familiarity with D'Alembert's principle
  • Knowledge of holonomic and semiholonomic systems
  • Concept of ideal and non-ideal constraints in mechanics
NEXT STEPS
  • Study the derivation and implications of Hamilton's principle in classical mechanics
  • Explore the differences between holonomic and semiholonomic constraints
  • Review D'Alembert's principle and its applications in dynamics
  • Investigate the characteristics and examples of ideal and non-ideal constraints
USEFUL FOR

This discussion is beneficial for students and professionals in physics, particularly those studying classical mechanics, as well as educators seeking to clarify concepts related to constraint forces and Hamiltonian dynamics.

Kashmir
Messages
466
Reaction score
74
Found a question on another website, I have the exact same question. Please help me

Goldstein says :
1631703142815.png


I do not understand how (2.34) shows that the virtual work done by forces of constraint is zero. How does the fact that "the same Hamilton's principle holds for both holonomic and semiholonomic systems" show that the additional forces of semiholonomic constraint do no work in the
##\delta q_k##

 
Physics news on Phys.org
Contraints that do zero net virtual work are sometimes called ideal constraints. Not all constraints are ideal (https://hal.archives-ouvertes.fr/hal-01399622/document)

Here Goldstein is asuming ideal constraints (the work of the forces of constraint do not appear in the right hand side of 2.34).
 
andresB said:
aints that do zero net virtual work are sometimes called ideal constraints. Not all constraints are ideal (https://hal.archives-ouvertes.fr/hal-01399622/document)
these guys completely do not understand what the D'Alembert-Lagrange is.
They think that they invented "nonideal constraints" but actually they consider systems with ideal constraints and given active forces applied. Some people begin to write articles before reading textbooks :)
 
Last edited:
  • Haha
Likes   Reactions: vanhees71
wrobel said:
these guys completely do not understand what the D'Alembert-Lagrange is.
They think that they invented "nonideal constraints" but actually they consider systems with ideal constraints and given active forces applied. Some people begin to write articles before reading textbooks :)
So what does the author mean? I still didn't get it
 

Similar threads

  • · Replies 7 ·
Replies
7
Views
1K
  • · Replies 16 ·
Replies
16
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 11 ·
Replies
11
Views
4K
  • · Replies 4 ·
Replies
4
Views
4K
  • · Replies 25 ·
Replies
25
Views
3K
  • · Replies 17 ·
Replies
17
Views
3K
  • · Replies 22 ·
Replies
22
Views
2K