This question pertains to engineering equations where the input into a function isn't "t".
Consider this one, it's describing rudder axle inertia:
$$J_t * \omega_t (t) = T_l (t) - B_t * \omega_t (t) + T_f * \omega ( \omega_t ) - T_sp ( \theta_t ) - T_l ( \delta_t ) $$ I can see how things like $ \mathcal{L} \,T_l (t) $ become $ T_L (s) $ ...but what about the other inputs from theta and omega?
...or is the formula just misformulated or incorrect in some other way?
Apologies for my attempt at formatting not working.