Page:PoincareDynamiqueJuillet.djvu/32

 This is why gave $$\tfrac{dD}{dV}$$ the name longitudinal mass and $$\tfrac{D}{V}$$ the name transverse mass; recall that $$D=\tfrac{dH}{dV}.$$

In the hypothesis of, we have:

$$\tfrac{\partial H}{\partial V}$$ represent the derivative with respect to V, after r and θ were replaced by their values as functions of V from the first two equations (1); we will also have, after the substitution,

We choose units so that the constant factor A is equal to 1, and I pose $$\sqrt{1-V^{2}}=h$$, hence:

We will pose again:

and we find the equation for quasi-stationary motion:

Let's see what happens to these equations by the transformation. We will pose: $$1+\xi\epsilon=\mu$$, and we have first:

from which we derive easily

We also have

where:

where again:

and