## anonymous 4 years ago I need help solving the following set of differential equations. This MUST be done in MATLAB. I can solve them otherwise, but I am struggling to accomplish this using MATLAB. ${dX_c \over dt} = v_x \cos(\theta) - v_y \sin(\theta)$${dY_c \over dt} = v_x \sin(\theta) + v_y \cos(\theta)$${d \theta \over dt} = \omega_z$ ${d v_x \over dt} = {1 \over m} \left [ F_x + mv_y \omega_z \right]$ ${d v_y \over dt} = {1 \over m} \left [ F_y - m v_x \omega_z \right]$ ${d \omega_z \over dt} = {1 \over I_z} T_{ext}$

The initial conditions are as follows: $$X_c(0) = 0 ; ~ Y_c(0) = 0; ~ \theta(0) = 0;~ v_x(0) = 0;~ v_y(0) = 0;~ \omega_z(0) = 0$$ The force and external torque have the following definition: $F_x(t) = 1000 \cos(0.1 t) ; ~ F_y = 100 \sin(0.2 t); ~ T_{ext} = 50(1 + \sin(0.3t))$Finally, $$m = 100~ {\rm and} ~ I_z = 1000$$