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
AndrĂ©
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