# Tag Info

Accepted

### What are holonomic and non-holonomic constraints?

If you have a mechanical system with $N$ particles, you'd technically need $n = 3N$ coordinates to describe it completely. But often it is possible to express one coordinate in terms of others: for ...
• 4,788
Accepted

### Hamiltonian for relativistic free particle is zero

...what I would like to know is why we get a zero Hamiltonian. I suspect that this is due to the reparametrization invariance... Will this always happen? Why? Yes, it is due to reparameterization ...
• 54.5k

### What are holonomic and non-holonomic constraints?

The question has been well-answered several times. I'll just add some geometrical context. In geometry, the holonomy group of a connection is the set of transformations an object can experience when ...
• 103k

### Confusion with Virtual Displacement

Here on SE, you may already find many answers to your question. Even if most of them are correct, I feel that a plain and correct answer is still missing. Where plain does not mean non-rigorous. But ...
Accepted

### Compute the Legendre transform for a singular Lagrangian

As a quick note, the equations of motion that come from that Lagrangian are $$\frac{d}{dt}\left(\dot q_1 + \dot q_2\right) = -2kq_1^3$$ $$\frac{d}{dt}\left(\dot q_2 + \dot q_1\right) = -2kq_2^3$$ ...
• 70.3k

• 208k
Accepted

### Virtual displacements

The main difference between "real" displacements and "virtual" displacements arise when the constraint itself is time-dependent. For example, you have an incline that is accelerating (I am saying ...
• 11.3k
Accepted

### Finding generalized coordinates when the implicit function theorem fails

Generally speaking, given a set of coordinates $x_1,\ldots,x_N$ under a set of $h=N-n$ holonomic constraints of the form $F_j(x_1,\ldots,x_N)=0$, you won't be able to find a subset $x_1,\ldots,x_n$ of ...
• 134k
Accepted

• 208k