# Conserved quantities in mechanics

1. Oct 25, 2012

### aaaa202

So having been through translation and rotation I can conclude that my book has found 3 conserved quantities in classical dynamics:
Energy
Angular momentum
Momentum
That is 7 separate quantities which are conserved E,Lx,Ly,Lz,px,py,pz
But this question is bothering me: How do we know that there are not more conserved quantities?

2. Oct 25, 2012

### AJ Bentley

Conservation laws come from invariance of the Lagrangian with each degree of freedom.
If you can think of another degree of freedom you can have another conservation law.

3. Oct 25, 2012

### Studiot

Is momentum always conserved?

Suppose I direct a hosepipe horizontally at a wall.

Please explain conservation of horizontal momentum at the wall face in this case.

4. Oct 25, 2012

### Staff: Mentor

In closed systems.

Some systems have additional conserved quantities, for example the Kepler problem or harmonic oscillators. But in the general case, you just have those 7 conserved quantities.

5. Oct 25, 2012

### Studiot

@mfb
Yes it is good to specify the conditions.
These were not originally specified and mechanics is not exclusively about closed systems, and should not be taught or thought of as such.

In my career I have seen spectacular failures of mechanical systems due to failure to appreciate this.

6. Oct 25, 2012

### D H

Staff Emeritus
Simple. The (effectively) infinitely massive wall moves at an (effectively) infinitesimally small rate. The product mass*velocity is some finite, non-zero quantity that exactly obeys conservation of momentum.

7. Oct 25, 2012

### Studiot

So where does the perpendicular (to the flow) momentum come from at the wall face?