Substitute specific expression that is not explicit in symbolic expression

I have a symbolic expression like this:

syms g                          % Gravitational acceleration
syms t                          % Time
syms m_1                         % Mass of Arm 1 
syms m_2                         % Mass of Arm 2

syms J_1                         % Moment of Inertia of Arm 1 about center of mass
syms J_2                         % Moment of Inertia of Arm 2 about center of mass

syms J_hat_1                         % Moment of Inertia of Arm 1 about origin of coordinate system 1 (pivot point)
syms J_hat_2                         % Moment of Inertia of Arm 2 about origin of coordinate system 2 (pivot point)

syms L_1                         % Length of Arm 1
syms L_2                         % Length of Arm 2
syms l_c_1                         % The length from the center of rotation of Arm 1 to its center of mass.
syms l_c_2                         % The length from the center of rotation of Arm 2 to its center of mass.
syms d_1                         % Viscous damping of Arm 1 (motor rotor)
syms d_2                         % Viscous damping of Arm 2 (between Arm 1 and Arm 2)
syms theta_1 
syms theta_dot_1 % Temporal derivative of Theta 1, the angular velocity of arm 1
syms theta_ddot_1 % Second temporal derivative of Theta 1, the angular acceleration of arm 1
syms theta_2 
syms theta_dot_2 % Temporal derivative of Theta 2, the angular velocity of arm 2
syms theta_ddot_2 % Second temporal derivative of Theta 2, the angular acceleration of arm 2
syms tau_1                        % Torque applied by motor on beam
syms tau_2                        % disturbance torque applied to arm 2

syms l_rot_1 % length between center of rotation and end of arm (positive x-direction)
syms l_rot_2 % length between center of rotation and end of arm (positive x-direction)

num = 8*J_1*tau_2 + 4*J_2*tau_2 + 4*l_c_2^2*m_2*tau_2 + 8*l_rot_1^2*m_1*tau_2 + 2*J_2^2*theta_dot_1^2*sin(2*theta_2) - J_2^2*theta_dot_1^2*sin(4*theta_2) - 4*J_2*tau_2*cos(2*theta_2) - 8*J_1*d_2*theta_dot_2 - 4*J_2*d_2*theta_dot_2 + 8*L_1^2*m_2*tau_2 + 4*J_1*J_2*theta_dot_1^2*sin(2*theta_2) + 2*l_c_2^4*m_2^2*theta_dot_1^2*sin(2*theta_2) - l_c_2^4*m_2^2*theta_dot_1^2*sin(4*theta_2) - 4*l_c_2^2*m_2*tau_2*cos(2*theta_2) - 6*g*l_c_2^3*m_2^2*sin(theta_2) - 8*L_1^2*d_2*m_2*theta_dot_2 - 4*d_2*l_c_2^2*m_2*theta_dot_2 - 8*d_2*l_rot_1^2*m_1*theta_dot_2 + 2*g*l_c_2^3*m_2^2*sin(3*theta_2) + 4*J_2*d_2*theta_dot_2*cos(2*theta_2) + 2*J_2*g*l_c_2*m_2*sin(3*theta_2) - 8*L_1^2*g*l_c_2*m_2^2*sin(theta_2) + 4*d_2*l_c_2^2*m_2*theta_dot_2*cos(2*theta_2) + 4*L_1^2*l_c_2^2*m_2^2*theta_dot_1^2*sin(2*theta_2) - 4*L_1^2*l_c_2^2*m_2^2*theta_dot_2^2*sin(2*theta_2) - 8*L_1*l_c_2*m_2*tau_1*cos(theta_2) - 8*J_1*g*l_c_2*m_2*sin(theta_2) - 6*J_2*g*l_c_2*m_2*sin(theta_2) + 4*J_2*L_1^2*m_2*theta_dot_1^2*sin(2*theta_2) + 4*J_1*l_c_2^2*m_2*theta_dot_1^2*sin(2*theta_2) + 4*J_2*l_c_2^2*m_2*theta_dot_1^2*sin(2*theta_2) - 2*J_2*l_c_2^2*m_2*theta_dot_1^2*sin(4*theta_2) + 4*J_2*l_rot_1^2*m_1*theta_dot_1^2*sin(2*theta_2) + 4*L_1*l_c_2^3*m_2^2*theta_dot_1*theta_dot_2*sin(theta_2) + 8*L_1*d_1*l_c_2*m_2*theta_dot_1*cos(theta_2) + 4*L_1*l_c_2^3*m_2^2*theta_dot_1*theta_dot_2*sin(3*theta_2) - 8*g*l_c_2*l_rot_1^2*m_1*m_2*sin(theta_2) + 4*l_c_2^2*l_rot_1^2*m_1*m_2*theta_dot_1^2*sin(2*theta_2) + 4*J_2*L_1*l_c_2*m_2*theta_dot_1*theta_dot_2*sin(theta_2) + 4*J_2*L_1*l_c_2*m_2*theta_dot_1*theta_dot_2*sin(3*theta_2)

I want to substitute then like this which does not work since subs does not reformulate before trying to subsitute:

subs(num, J_2 + m_2*(l_c_2)^2, J_hat_2)

The purpose is to introduce simplifying variables very much like subexpr does but with my own custom terms.

Thanks in advance for any help!