Computer Science
Scientific paper
Dec 1982
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1982cemec..28..367b&link_type=abstract
Celestial Mechanics, Volume 28, Issue 4, pp.367-380
Computer Science
10
Scientific paper
Conditions are found which are satisfied by the coefficients of the expressionΦ = Adot x^2 + 2Bdot xdot y + + Γ dot y^2 + Δ dot x^2 dot y^2 + E being a second integral of the motion of an autonomous dynamical system with two degrees of freedom. The coefficientsA, B. Γ, Δ,E are differentiable functions of the cartesian position coordinatesx, y. The velocity components are denoted bydot x,dot y. It is shown that Δ must be constant andB must be of the formB =f(x+y) +g(x-y) wheref, g are arbitrary. Given Δ andB one can always find the remaining coefficientsA, ΓE and also the corresponding potential and second integral. Depending on the specifica case at hand a certain number of arbitrary constants (or arbitrary functions) enter into the potential and the second integral. To each potential (which may be of the separable or nonseparable type in the coordinatesx andy)there corresponds one integral of the above form.
No associations
LandOfFree
Compatibility Conditions for a Non-Quadratic Integral of Motion 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 Compatibility Conditions for a Non-Quadratic Integral of Motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Compatibility Conditions for a Non-Quadratic Integral of Motion will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-928899