could you upload your file that works first, it will help me to understand and appreciate your question better.

currently, it does not compile.

glad you are also using EJS. :) We are not alone! welcome to this community

variable double theta_A_double_dd

commented
//theta_A_dd + (y_dd+g)/l_p*Math.sin(theta_A) + l*phi_dd/l_p*Math.sin(phi+theta_A) + (l/l_p)*phi_d^2*Math.cos(phi+theta_A) = 0;
//theta_B_dd + (y_dd+g)/l_p*Math.sin(theta_B) - l*phi_dd/l_p*Math.sin(phi+theta_B) + (l/l_p)*phi_d^2*Math.cos(phi+theta_B) = 0;
// y_dd + 2*k/(M+2*m)*y + m*l_p/(M+2*m)*(theta_A_dd*Math.sin(theta_A) + theta_A_d^2*Math.cos(theta_A) + theta_B_dd*Math.sin(theta_B) + theta_B_d^2*Math.cos(theta_B)) + g = 0;
//phi_dd + g/l*Math.cos(phi) + k/m*Math.sin(phi)*Math.cos(phi) + (theta_A_dd*Math.sin(phi+theta_A) + l_p/(2*l)*theta_A_d^2*Math.cos(phi+theta_A) - theta_B_dd*Math.sin(phi+theta_B) - theta_B_d^2*Math.cos(phi+theta_B)) = 0;

i suspect you can't assign
theta_A_dd + (y_dd+g)/l_p*Math.sin(theta_A) + l*phi_dd/l_p*Math.sin(phi+theta_A) + (l/l_p)*phi_d^2*Math.cos(phi+theta_A) = 0;

the programming syntax says to assign a value of 0 to theta_A_dd + (y_dd+g)/l_p*Math.sin(theta_A) + l*phi_dd/l_p*Math.sin(phi+theta_A) + (l/l_p)*phi_d^2*Math.cos(phi+theta_A) .

that's is all i can help :) i don't know how to solve your problem yet!