A new look at the simple pendulum

A simple formula for the large-angle pendulum period

“…Some excellent introductory textbooks 3,4 simply cite a series approximation, but we feel that some justification is desirable and a series derivation may be a bit advanced for first-semester students. The ingenious strategies of Santarelli et al, 5 Molina, 6 Ganley, 7 and Caldwell and Boyco 8 are a little too involved for our purposes, and we believe we have contrived a simpler intuitive approach.…”

A comprehensive analytical solution of the nonlinear pendulum

“…In recent years, some effort has been made to solve this differential equation by means of approximations, JACOBI elliptic functions and hypergeometric functions; see e.g. [4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Whereas most papers are limited to a pendulum that does not swing over, one can find in [16] and [17] also a solution for a pendulum that swings over.…”

Pendulum state estimation using nonlinear state estimators

“…Acceleration of a simple pendulum with a unit mass and suspended by a unit length (L=1) string is defined through a continuous time nonlinear differential equation which is given by [1,7] …”

“…A suspended metal massy object (bob) with a string attached to a rigid support is the simple pendulum schematic shown in fig 1 [1,9]. The path of bob having three major points, equilibrium position and two maximum positions as back and forth.…”