ofn bodies finite rotations problem kinetic frame article reduced manifold variables system automatic processing functional language Mathieu canonical transformation Elimination of the nodes in problems ofn bodies elimination quadruple https://scigraph.springernature.com/explorer/license/ quaternions top trees body frame manifold language vector base reduction theorem 1983-06-01 In application of the Reduction Theorem to the general problem ofn (>-3) bodies, a Mathieu canonical transformation is proposed whereby the new variables separate naturally into (i) a coordinate system on any reduced manifold of constant angular momentum, and (ii) a quadruple made of a pair of ignorable longitudes together with their conjugate momenta. The reduction is built from a binary tree of kinetic frames Explicit transformation formulas are obtained by induction from the top of the tree down to its root at the invariable frame; they are based on the unit quaternions which represent the finite rotations mapping one vector base onto another in the chain of kinetic frames. The development scheme lends itself to automatic processing by computer in a functional language. coordinate system rotation false nodes en articles frames Explicit transformation formulas ignorable longitudes kinetic frames Explicit transformation formulas binary tree theorem 1983-06 problems ofn bodies transformation longitude reduction https://doi.org/10.1007/bf01234305 roots unit quaternions applications invariable frame computer processing constant angular momentum conjugate momenta development schemes momentum base Explicit transformation formulas general problem chain new variables angular momentum 2021-12-01T19:05 induction pairs canonical transformation 181-195 formula transformation formula scheme National Bureau of Standards, DC 20234, Washington, USA National Bureau of Standards, DC 20234, Washington, USA André Deprit pub.1047310995 dimensions_id 10.1007/bf01234305 doi Applied Mathematics Springer Nature - SN SciGraph project Celestial Mechanics and Dynamical Astronomy 0923-2958 0008-8714 Springer Nature Mathematical Sciences 30 2