replace expression of variables with an equivalent variable?

Hi,

how can i get back theta_v instead of omega*t + phi_v?

% Code
clearvars; clc;
syms  Vx                  positive 
syms  theta_v phi_v 
syms  omega t             positive
theta_v = omega*t + phi_v;
v = Vx*sin(theta_v)
y = diff(v, t)
subs(y,omega*t + phi_v, theta_v)

Answer 1

[Karan Gill]

Your substitution can't work because you defined "theta_v" to be "omega*t + phi_v". So you're just substituting "omega*t + phi_v" for the same thing. If you want to keep "theta_v" then don't define it as "omega*t + phi_v". Keep it as a symbolic function, and substitute in at the end.

>> syms x
>> syms theta_v(t)
>> syms Vx
>> v = Vx*sin(theta_v)
v(t) =
Vx*sin(theta_v(t))

>> y = diff(v, t)
y(t) =
Vx*cos(theta_v(t))*diff(theta_v(t), t)

>> syms omega phi_v
>> subs(y,theta_v, omega*t + phi_v)
ans(t) =
Vx*omega*cos(phi_v + omega*t)