The Equations of Relative Motion of Systems of Bodies on Superphysics

The Relative vis viva Equation

Thu, 21 May 2026 00:00:00 +0000

The principle of vis viva (living forces) can be applied to the relative arbitrary motions in coordinate planes.

This can be done by adding to the given forces other forces that are opposed to those capable of forcing the material points to remain invariably linked to the moving planes to which the relative motions are referred.

The Relative vis viva Equation

Thu, 21 May 2026 00:00:00 +0000

These second forces disappear in the equation of vis viva just as ordinary centrifugal forces do, since they are directed perpendicularly to the relative velocities, and the equation of vis viva is obtained only by projecting the forces onto the direction of the relative velocities themselves.

The Center of Gravity

Thu, 21 May 2026 00:00:00 +0000

Finally, if the center of gravity moves along a line given with respect to the moving plane; by taking the axis of ζ for this line, we have $\frac{d\eta}{dt} = 0$ , $\frac{d\xi}{dt} = 0$ , and consequently,