Physics – Classical Physics
Scientific paper
2010-07-22
Physics
Classical Physics
Scientific paper
In this work we solve the nonlinear second order differential equation of the simple pendulum with a general initial angular displacement ($\theta(0)=\theta_0$) and velocity ($\dot{\theta}(0)=\phi_0$), obtaining a closed-form solution in terms of the Jacobi elliptic function $\text{sn}(u,k)$, and of the the incomplete elliptical integral of the first kind $F(\varphi,k)$. Such a problem can be used to introduce concepts like elliptical integrals and functions to advanced undergraduate students, to motivate the use of Computer Algebra Systems to analyze the solutions obtained, and may serve as an exercise to show how to carry out a simple generalization, taking as a starting point the paper of Bel\'endez \emph{et al} \cite{belendez}, where they have considered the standard case $\dot{\theta}(0)=0$.
Juchem Neto J. P.
No associations
LandOfFree
Nonlinear Pendulum: A Simple Generalization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Nonlinear Pendulum: A Simple Generalization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonlinear Pendulum: A Simple Generalization will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-138375