solving Differential Equations

I have following Differential Equations

a1*x2+b2*x1-c*cos(int(x3))*x4=d
-c*cos(int(x3))*x2-a2*sin(int(x3))+b2*x4=0

where a1,b2,c,d,a2,b2 are constants and x1=theta_dot; x2=theta_ddot; x3=alpha_dot; x4=alpha_ddot

I want to solve these equations for x1,x2,x3,x4 and want to plot with time.

Answer 1

[Grzegorz Knor]

How Do I Reduce the Order of an ODE?

[Vijay Marathe]

thanks, but I don't want to reduce the order of system.

how to solve for given input Vm, it may be ramp, step, const. input

eqs are

a1*x2+b2*x1-c*cos(int(x3))*x4=d*Vm

-c*cos(int(x3))*x2-a2*sin(int(x3))+b2*x4=0

I want plot x1,x2,x3,x4 with respect time.

[Grzegorz Knor]

You have to reduce to a system to first-order ODEs, because ode solvers solve ony first-order ODEs.

Answer 2

[Walter Roberson]

Do you mean:

a1*x2(t)+b2*x1(t)-c*cos(int(x3(t), t))*x4(t) = d*Vm,
-c*cos(int(x3(t), t))*x2(t)-a2*sin(int(x3(t), t))+b2*x4(t) = 0

If so then there is no solution, or perhaps no solution without further information. 2 equations in 4 unknowns is seldom enough to be able to what the functions are, let alone the boundary conditions.

[Grzegorz Knor]

Author in his first post wrote, that there are dependencies between x1 and x2 and between x3 and x4. But still there is lack of the initial and boundary conditions.

[Walter Roberson]

If x1 and x2 are functions of theta, then one cannot solve for them directly: one would have to express the functions in full first, solve the DE, and then construct x1 and x2 (and x3 and x4) from the results.