What Are Degrees of Freedom and Why Do They Matter?

[cks]

What do you understand about this?

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.

 

[cristo]

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.

 

[cks]

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

 

[DaveC426913]

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.

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

 

[stewartcs]

Surely there are only five...

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

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

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

 

[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.

 

[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.)

 

[Dale]

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

 

[tabchouri]

agreed with that DaleSpam, 3 angles are needed to uniquely define the position in 3d.
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[pmb_phy]

What do you understand about this?

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.

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