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unable to solve non linear differential equation

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Muhammad Shoaib
Muhammad Shoaib on 26 Feb 2021
Answered: Bjorn Gustavsson on 26 Feb 2021
Please help me solving following differential equation. I have attached matlab code. When i run this code it gives solution "Unable to find explicit solution."
syms r(t) omega meu theta g;
Dt = diff(r,t);
D2t = diff(r,t,2);
ode = D2t - (r*(omega^2)*(sin(theta))^2)+(meu*sin(theta)*((4*(omega^2)*(Dt)^2)+(g-cos(theta))^2)^(1/2))+(g*cos(theta)) == 0;
cond1 = r(0)==0.001;
cond2 = Dt(0)==0;
cond3 = D2t(0)==0;
cond = [cond1 cond2 cond3];
rsolt = dsolve(ode, cond)

Answers (1)

Bjorn Gustavsson
Bjorn Gustavsson on 26 Feb 2021
This looks like an equation of the form:
Unless you have an equation for a trajectory of a spinning object falling in gravity...
Anyhow, that ODE has as far as I was taught no simple analytical solution, so you have to integrate it numerically. See the help and documentation for ode45 and the numerous examples and demos for how to solve coupled ODEs numerically.

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