# Degree of freedom

1. Oct 21, 2007

### cks

From high school, I just memorize the definition of it, the number of ways of obtaining energy independently. Well, it's pretty unclear by this definition.

2. Oct 21, 2007

### cristo

Staff Emeritus
Perhaps you could tell us more precisely the problem you have encountered with using degrees of freedom. To put it simply, the number of degrees of freedom of a system are the minimum number of parameters you need in order to describe the system uniquely. So, for example, a point in 3 dimensional space has 3 degrees of freedom (one for each of the three dimensions). If we state which value in each dimension the point has (i.e. define the coordinate (x,y,z)) then we have uniquely specified where in space that point is. An object in 3 dimensional space has 6 degrees of freedom: three defining its position in space, and 3 defining the angles of rotation. Again, if we specify these 6 parameters, then we have uniquely described the system.

3. Oct 21, 2007

### cks

For your second explanation, why there are 3 angles of rotation to specify the system. ?

4. Oct 21, 2007

### DaveC426913

Surely there are only five. I think you can uniquely describe the angle of rotation of an object using only two angles of rotation.

5. Oct 21, 2007

### stewartcs

For a rigid body in three-space there are indeed six possible degrees of freedom.

In most cases I would agree that you are correct indeed.

6. Oct 21, 2007

### christianjb

I think it's helpful to distinguish between 'quadratic' DOF and 'free' DOF.

Yes- rotation of an object is in general determined by 3 DOF, which could be expressed as 2 polar coordinates and 1 rotation about the axis. A diatomic molecule only has 2 rotational axes because it is symmetric about the last rotation.

7. Oct 21, 2007

### DaveC426913

I meant objects that have no rotational symmetry. They can be oriented in any of three directions by rotation aroind only two axes.

Wait... I just demonstrated that it DOES take 3 DoFs to uniquely describe an object. (though it may only require two to GET it there.)

8. Oct 21, 2007

### Staff: Mentor

Yaw, pitch, roll. There are three. I think you were probably just forgetting roll.

9. Oct 21, 2007

### tabchouri

10. Oct 21, 2007

### pmb_phy

By definition, the degrees of freedom is the minimum number of variables required to uniquely define the mechanical configuration of thhe system. E.g. a double pendulum has two degress of freedom. Two variables that might be chosen are the angle each pendulum makes with the vertical.

Best wishes

Pete