Isolating integral (source code)

= Isolating integral

An isolating integral is a regular single-valued <integral of motion> whose fixed value restricts accessible <phase space> to a lower-dimensional level set. Functional independence of several such integrals means their differentials are linearly independent on the region considered. A central potential has <specific orbital energy> and the three components of <specific angular momentum> as four generically independent integrals. A <Kepler orbit> has a fifth independent integral supplied by its fixed apsidal direction, encoded by the <Laplace-Runge-Lenz vector>; its vector components obey two constraints with energy and angular momentum. Circular and radial orbits are degenerate cases of this count.