The method of the apparent vertical applied to pendulum dynamics

dc.creator	Héctor A. Múnera
dc.creator	Héctor R. Maya
dc.date	2011-03-01T00:00:00Z
dc.date.accessioned	2015-07-20T22:11:48Z
dc.date.available	2015-07-20T22:11:48Z
dc.identifier	1870-9095
dc.identifier	https://doaj.org/article/de48df2e22a2456fad7361a49d90d1ee
dc.identifier.uri	http://evidence.thinkportal.org/handle/123456789/14717
dc.description	The paper describes the geometrical method of the apparent vertical (MAV for short) for the solution of a large class of problems in elementary classical mechanics: perturbation of a dynamical system by a constant or nearly constant force, not necessarily small. The basic idea is to rotate the system of coordinates so that the z-axis coincides with an ―apparent‖ acceleration of gravity. The solution in the rotated system is simpler than in the unrotated coordinates, and it is usually known. The methodology is illustrated with a spherical pendulum in a uniform field of force, where the standard solution in terms of elliptic functions is directly applicable in the rotated system of coordinates. The trajectory of the bob in the usual coordinates attached to the laboratory is obtained by a straightforward rotation of coordinates, thus allowing calculation of the observable parameters: amplitude, period, and plane of oscillation of the pendulum.
dc.language	English
dc.language	Spanish
dc.language	Portuguese
dc.publisher	Instituto Politécnico Nacional, Latin American Physics Education Network
dc.relation	http://www.lajpe.org/march11/LAJPE_468_Hector_Munera_preprint_corr_f.pdf
dc.relation	https://doaj.org/toc/1870-9095
dc.source	Latin-American Journal of Physics Education, Vol 5, Iss 1, Pp 22-30 (2011)
dc.subject	spherical pendulum dynamics
dc.subject	perturbed dynamical systems
dc.subject	geometrical solution of equations of motion
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	DOAJ:Education
dc.subject	DOAJ:Social Sciences
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.subject	Special aspects of education
dc.subject	LC8-6691
dc.subject	Education
dc.subject	L
dc.title	The method of the apparent vertical applied to pendulum dynamics
dc.type	article