First integrals for the modified Emden equation q̈+α(t) q̇+q n =0
- 1 October 1985
- journal article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 26 (10) , 2510-2514
- https://doi.org/10.1063/1.526766
Abstract
It is shown that the modified Emden equationq̈+α(t)q̇+q n =0 possesses first integrals for functions α(t) other than k t − 1. The function α(t) is obtained explicitly in the case n=3 and parametrically for other n(≠2). The case n=2 is seen to be particularly difficult to solve.Keywords
This publication has 5 references indexed in Scilit:
- A direct approach to finding exact invariants for one-dimensional time-dependent classical HamiltoniansJournal of Mathematical Physics, 1982
- Generalizations of Noether’s Theorem in Classical MechanicsSIAM Review, 1981
- Schrödinger equation with time-dependent boundary conditionsJournal of Mathematical Physics, 1981
- A direct construction of first integrals for certain non-linear dynamical systemsInternational Journal of Non-Linear Mechanics, 1980
- Note on the time-dependent damped and forced harmonic oscillatorAmerican Journal of Physics, 1978