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Forgive me if this is considered reposting, but I've been advised I might have given a bad format.

I'm trying to solve the two linear, second order differential equations. I want to break them into single order equations, but I can't see how as both variables have second order derivatives in both problems.

(m*a)u” + (I + m*a^2 )θ” + (d*a^2 )θ’ + (K - m*g*a)θ = 0

(M + m)u” + (m*a)θ” = -F

I've gone to some lengths with both dsolve and ode45

This is my dsolve code:

M =70-5.876;
m =5.876;
a =(((0.05)^2)+((0.13^2))^0.5);
IG = 0.0233;
d = 500;
k = 500;
g = 9.81;
f = 628;

%y is u, x is theta

syms M m a IG d k g y(t) x(t)
Dy = diff(y);
Dx = diff(x);

eqn1 = (M+m)*diff(y,2) + M*diff(x,2) == -f;

eqn2 = m*a*diff(y,2) + (IG + m*a*a)*diff(x,2) + (d*a*a)*diff(x) + (k - m*g*a)*x == 0;

t=0:0.01:10;

z = dsolve(eqn1,eqn2, y(0)==0, Dy(0)==0, x(0)==0, Dx(0)==0, 't');

z.x
z.y

It does give me very, very long equations that I can't seem to plot with respect to time and I don't know why. If anyone can advise me I'd be very grateful. Thanks for looking!

user2101633
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1 Answers1

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In this case u" can be replaced out of the general equation with simple algebraic manipulation. The resulting equation will be of the order:

Eq1: K1*θ” + K2*θ’ + K3*θ = -F

u can be solved directly with the solution of Eq1. Try to avoid placing u in the equation. If you must, you'll need to rewrite the equations so as to solve with the third differential of θ.

Rasman
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