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spherical pendulum - lagrange mechanics - theoretical physics

version (196 KB) by Lucas Tassilo Scharbrodt
solve the equations of motion and plot the pendulum's trajetory


Updated 11 Jul 2018

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The problem is a nice simple example which can be found in any textbook on Theoetical Mechanics.
The position of the pendulum is described by two generalized coordinates (in spherical polar coordinates) theta and phi (r is constant). Using Lagrange2 equation a system of two second order nonlinear ordinary differential equations arises, which first has to be linearized to a system of 4x now first order ODEs in order to then be solved numerically by one of the matlab buildin solvers.
Here are the lines of code i'm refering to:
y10 = [0.4*pi 0 0 1.5]; % Initial Conditions for [ theta theta' phi phi'] at time t=0
f = @(t,y)[y(2);(( y(4))^2).*sin(y(1)).*cos(y(1))-(g/R).*sin(y(1)) ; y(4);-2.*(cos(y(1)).*y(2).*y(4))./(sin(y(1)))];
[t,y] = ode45(f,tspann,y10); % call ODE45 solver

Cite As

Lucas Tassilo Scharbrodt (2022). spherical pendulum - lagrange mechanics - theoretical physics (, MATLAB Central File Exchange. Retrieved .

MATLAB Release Compatibility
Created with R2017b
Compatible with any release
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