Solve symbolic equation for a variable which itself is a function of time

Hello

I am trying to solve a symbolic equation for the variable, theta_ddot.

I have defined the angle (theta) and acceleration (theta_ddot) as time dependant, which seems to cause a problem when I try to solve the equation symbolically. MATLAB give the warning: "Warning: Unable to find explicit solution. For options, see help"

I have tried to not define theta and theta_ddot as time dependant which solves the problem. However I need them to be time dependant since I have to take the time derivative later on so I can't do that.

I have attached my code below

syms m a J theta_ddot(t) theta(t) tau_1 g eq1
eq1 = (m*a^2 + J) * theta_ddot + a*g*m*cos(theta)

eq1(t) = 

S = solve(tau_1 == eq1,theta_ddot)

Warning: Unable to find explicit solution. For options, see help.

S = struct with fields:
        t: [0×1 sym]
    tau_1: [0×1 sym]

Hope someone can help explain what seems to be the problem. :)

Thanks in advance

Answer 1

[Steven Lord]

If you're trying to solve a differential equation, try using dsolve instead of solve.

[Christian Noerkjaer]

That unfortunately does not seem to help. Since the equation does not contain a derivative as matlab would understand it, it seems dsolve can't do the trick. I would very much like to avoid substituting the theta_ddot term back to the double partial derivative of theta.

syms m a J theta_ddot(t) theta(t) tau_1 g eq1
eq1 = (m*a^2 + J) * theta_ddot + a*g*m*cos(theta)

eq1(t) = 

S = dsolve(tau_1 == eq1,theta_ddot)

Error using symengine
No differential equations found. Specify differential equations by using symbolic functions.

Error in mupadengine/evalin_internal

Error in mupadengine/fevalHelper

Error in mupadengine/feval_internal

Error in dsolve>mupadDsolve (line 334)
T = feval_internal(symengine,'symobj::dsolve',sys,x,options);

Error in dsolve (line 203)
sol = mupadDsolve(args, options);

[Walter Roberson]

syms m a J theta_ddot(t) theta(t) tau_1 g eq1
theta_dot = diff(theta);
theta_ddot = diff(theta_dot);
eq1 = (m*a^2 + J) * theta_ddot + a*g*m*cos(theta)

eq1(t) = 

S = dsolve(tau_1 == eq1)

S = 

tdd = diff(S, t, t)

tdd = 

simplify(tdd, 'steps', 50)

ans = 

Derivative of union is not a good sign.

In the final result, the reason for there to be a conditional on the 0 and for there to be no other values, is that it is MATLAB's way of saying that the solution can be defined as 0 under those particular cases, but is otherwise undefined.