Recent content by Last-cloud

yes , i have a problem ; \begin{equation} m_{z}\ddot{w}+EIw'''-Tw''-f+c_{1}\dot{w}-EAv''w'-EAv'w''-\dfrac{3}{2}EA(w')^2w''=0 \end{equation} \begin{equation} m_{z}\ddot{v}+c_{2}\dot{v}-EAv''-EAw'w''=0 \end{equation} the boundary conditions of the system : \begin{equation}...

i want to solve a nonlinear PDE with finite difference method ,but using just discretization like in linear PDE , it will lead to nowhere , what's the right way to use FDM to solve nonlinear PDE or could someone provide me with book's titles or articles that can help me solving a nonlinear pdf...

the system that I'm applying Hamilton's Principle to , is the Lagrangian "L" such that \begin{equation} \begin{split} L&=E_{k}-E_{p}+W=\\ &\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ \left( \dfrac{\partial w(x,t)}{\partial t}\right)^{2}+\left( \dfrac{\partial...

I want to obtain equation using Hamilton principle but I just couldn't figure it out; i have The kinetic energy : \begin{equation} E_{k}=\dfrac{1}{2}m_{z} \displaystyle\int\limits_{0}^{L}\ \left[ \left( \dfrac{\partial w(x,t)}{\partial t}\right)^{2}+\left( \dfrac{\partial v(x,t)}{\partial...