Journal of Mathematical Physics · 1996 · 93 citations · 4 references
Natural SciencesMathematicsPhysicsDynamical SystemsGeometryOrbital MechanicsGroup TheoryGroup Theory In PhysicsKeplerian MotionKeplerian OrbitsLie GroupsOrbital DynamicsKepler EquationKepler ProblemOrbital GeometrySymmetriesSymmetry AnalysisSymmetry Groups In Spacetime
It is shown that the complete symmetry group for the Kepler problem, as introduced by Krause, can be derived by Lie group analysis. The same result is true for any autonomous system.
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Applications of lie groups to differential equations
Acta Applicandae Mathematicae · 1990 · 6.1K citations
Group Analysis of Differential Equations.
Willard Miller · American Mathematical Monthly · 1985 · 2.5K citations
<i>Nonlinear Partial Differential Equations in Engineering</i>
W.F. Ames, J. Gillis · Physics Today · 1967 · 749 citations