lagrange_eq(T,V,Q,F​0,r_F,fun_name,vara​rgin)

Lagrange equation of motion

% lagrange_eq is a function that calculate equations of motion (Lagrange's
% equations) and create a function file to uses with Matlab ode functions.
% The Lagrangian L is separated in T and V, L= T - V, and adds dissipation
% function Q (viscous damper) and generalized force:
% d/dt(dT/d(dq) + dV/dq + dQ/d(dq) = F0
% Symbolic Math Toolbox is required.
%
%
% Usage as:
% lagrange_eq(T,V,Q,F0,r_F,fun_name,q1,q2,...,qn)
%
% T = Kinetic Energy
% V = Potencial Energy
% Q = Dissipated Energy
% F0 = Generalized Force
% r_F = point of force aplication
% fun_name = name of the ode function fun_name.m
% q1 = firts DOF
% q2 = second DOF
% qn = last DOF
%
% T, V, Q, F0 are symbolics functions, q1,q2,..,qn are time-dependent
%
% ******* Example 1 *********
% Mass-Spring-Damper
% 1 DOF
% syms x(t) t m k c f omega
% T = 1/2*m*diff(x)^2;
% V = 1/2*k*x^2;
% Q = 1/2*c*diff(x)^2;
% F = f*sin(omega*t);
% r_F = x(t);
%
% lagrange_eq(T,V,Q,F,'fun_mass_spring_damper',x)
% m = 10; % [kg]
% k = 10; % [N/m]
% c = 100; % [Ns/m]
% f = 50; % [N]
% omega = 10*2*pi; % [rad/s]
%
% [t,x]=ode45(@(t,z) fun_mass_spring_damper(t,z,c,f,k,m,omega) , [0 T_r] , [Xo;DXo]);
%
% ******* Example 2 *********
%
% 2 DOF
% syms x(t) y(t) t m k c f omega
% T =...;
% V =...;
% Q =...;
% F = [f*cos(omega) f*sin(omega)];
% r_F = [x(t) y(t)];
%
% lagrange_eq(T,V,Q,F,r_F,'fun2',x,y)
%
% ******* Example 3 *********
% 5 DOF
% syms q1(t) q2(t) q3(t) q4(t) q5(t) t m k c f omega
% T =...;
% V =...;
% Q =...;
% F =...;
% r_F = ...;
% lagrange_eq(T,V,Q,F,r_F,'fun2',q1,q2,q3,q4,q5)