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On the Motion of the Pendulum on an Ellipse
Author(s) -
ElBarki F.A.,
Ismail A.I.,
Shaker M.O.,
Amer T.S.
Publication year - 1999
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/(sici)1521-4001(199901)79:1<65::aid-zamm65>3.0.co;2-x
Subject(s) - ellipse , pendulum , motion (physics) , double pendulum , equations of motion , point (geometry) , kapitza's pendulum , mathematics , inverted pendulum , classical mechanics , mathematical analysis , path (computing) , physics , geometry , computer science , nonlinear system , quantum mechanics , programming language
In the present study, the motion of a pendulum on an ellipse is considered. The supported point of this pendulum moves on an elliptic path while the end point moves with arbitrary angular displacements. Applying Lagrange's equation, the equation of motion is obtained in terms of a small parameter ε. This equation represents a quasilinear system of second order which can be solved in terms of a generalized coordinate φ.