TY - JOUR
T1 - Approximate frequencies of the pendulum for large angles
AU - Salinas-Hernández, E.
AU - Ares De Parga, G.
AU - Domínguez-Hernández, S.
AU - Muñoz-Vega, R.
N1 - Publisher Copyright:
© 2017, Sociedad Mexicana de Fisica. All rights reserved.
PY - 2017/1/1
Y1 - 2017/1/1
N2 - By approximating the cosine function to a polynomial, analytical approximations of pendulum trajectories are developed for initial angles close to π. The periods are deduced and they are compared with other techniques recently developed for the same purpose. Our results practically match with the exact solutions. A process that allows to understand the difficulties of dealing with nonlinear equations, of using the minimization of the standard deviation and the importance played by energy conservation is done.
AB - By approximating the cosine function to a polynomial, analytical approximations of pendulum trajectories are developed for initial angles close to π. The periods are deduced and they are compared with other techniques recently developed for the same purpose. Our results practically match with the exact solutions. A process that allows to understand the difficulties of dealing with nonlinear equations, of using the minimization of the standard deviation and the importance played by energy conservation is done.
KW - Frequency
KW - Pendulum
KW - Polynomial
UR - http://www.scopus.com/inward/record.url?scp=85007462340&partnerID=8YFLogxK
M3 - Artículo
SN - 1870-3542
VL - 63
SP - 6
EP - 11
JO - Revista Mexicana de Fisica E
JF - Revista Mexicana de Fisica E
IS - 1
ER -