Mathematics – Logic
Scientific paper
Aug 2003
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2003dda....34.0902n&link_type=abstract
American Astronomical Society, DDA meeting #34, #09.02; Bulletin of the American Astronomical Society, Vol. 35, p.1042
Mathematics
Logic
Scientific paper
The method of variation of constants is an important tool used to solve systems of ordinary differential equations, and was invented by Euler and Lagrange to solve a problem in orbital mechanics. This methodology assumes that certain ``constants'' associated with a homogeneous problem will vary in time in response to an external force. It also introduces one or more constraint equations motivated by the nature of the time-dependent driver. We show that these constraints can be generalized, in analogy to gauge theories in physics, and that different constraints can offer conceptual advances and methodological benefits to the solution of the underlying problem. Examples are given from linear ordinary differential equation theory and from orbital mechanics. However, a slow driving force in the presence of multiple time scales contained in the underlying (homogeneous) problem nevertheless requires special care, and this has strong implications to the analytic and numerical solutions of problems ranging from celestial mechanics to molecular dynamics.
Efroimsky Michael
Newman William I.
No associations
LandOfFree
The Method of Variation of Constants and Multiple Time Scales in Orbital Mechanics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with The Method of Variation of Constants and Multiple Time Scales in Orbital Mechanics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Method of Variation of Constants and Multiple Time Scales in Orbital Mechanics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-1667757