# Hamilton's principle and virtual work by constraint forces

• A
• Kashmir
In summary, Goldstein is discussing the concept of ideal constraints and how they apply to Hamilton's principle for both holonomic and semiholonomic systems. The author also mentions the confusion surrounding the concept of nonideal constraints, which are often misunderstood. They suggest that some people write articles before fully understanding the topic.
Kashmir
Found a question on another website, I have the exact same question. Please help me

Goldstein says :

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##

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:
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

## 1. What is Hamilton's principle and how does it relate to virtual work by constraint forces?

Hamilton's principle states that the motion of a mechanical system can be described by the principle of least action, where the system will follow the path that minimizes the action integral. This principle is closely related to virtual work by constraint forces, as it considers the forces acting on a system and their corresponding virtual displacements in order to determine the path of least action.

## 2. How are constraint forces treated in Hamilton's principle?

Constraint forces are treated as virtual forces in Hamilton's principle, meaning that they do not actually exist in the system but are considered in order to determine the path of least action. These virtual forces arise from constraints that restrict the motion of the system, such as fixed points or rigid connections.

## 3. What is the significance of virtual work in Hamilton's principle?

Virtual work is a key concept in Hamilton's principle, as it allows for the consideration of forces that do not actually exist in the system. By considering the virtual work done by constraint forces, the principle of least action can be applied to determine the path of motion for a mechanical system.

## 4. How is Hamilton's principle applied in real-world scenarios?

Hamilton's principle can be applied in a variety of real-world scenarios, such as in engineering and physics. It is often used in the analysis of mechanical systems, such as in the design of structures or machines, to determine the most efficient path of motion.

## 5. What are the limitations of Hamilton's principle and virtual work by constraint forces?

One limitation of Hamilton's principle is that it assumes the system is in equilibrium, meaning that the forces acting on it are balanced. Additionally, it may not be applicable in systems with complex or non-linear constraints. Virtual work by constraint forces also does not take into account dissipative forces, such as friction, which can affect the motion of a system.

### Similar threads

• Mechanics
Replies
7
Views
730
• Mechanics
Replies
16
Views
2K
• Mechanics
Replies
14
Views
1K
• Mechanics
Replies
6
Views
2K
• Classical Physics
Replies
3
Views
818
• Mechanics
Replies
6
Views
2K
• Classical Physics
Replies
25
Views
1K
• Mechanics
Replies
11
Views
3K
• Mechanics
Replies
4
Views
3K
• Classical Physics
Replies
17
Views
2K