For a rigid body the kinetic energy will, in general, consist of three terms (AW1 2 +BW2 2 +CW3 2) in addition to the translational energy.
The previous treatment of the motion of a rigid body had in every case been purely analytical, and so gave no aid to the formation of a mental picture of the body's motion; and the great value of this work lies in the fact that, as Poinsot himself says in the introduction, it enables us to represent to ourselves the motion of a rigid body as clearly as that of a moving point.
For Diatomic Or Compound Gases Clerk Maxwell Supposed That The Molecule Would Also Possess Energy Of Rotation, And Endeavoured To Prove That In This Case The Energy Would Be Equally Divided Between The Six Degrees Of Freedom, Three Of Translation And Three Of Rotation, If The Molecule Were Regarded As A Rigid Body Incapable Of Vibration Energy.
At a later stage in our subject the conception of the ideal rigid body is introduced; this enables us to fill in some details which were previously wanting, but others are still omitted.
Hence a rigid body not constrained in any way is said to have six degrees of freedom.
