How to solve for center of mass position change and rotation as a result of the same moment?

I have created a way of solving for an objects trajectory with the standard force sum introduced in kinematics.

classdef pointmass
    properties
        mass
        position
        velocity
        orientation
        translation_force_sum
    end
    methods
        function [position, velocity] = solve(obj,dt)
            a = obj.translation_force_sum/obj.mass;
            velocity = obj.velocity + a*dt;
            position = obj.position + obj.velocity*dt;
        end
    end
end

The result for a trivial case (zero forces) is an object that follows its initial trajectory, and for a case with only gravity, an object that follows the familiar parabolic trajectory. I know from experience that if, for example, a rocket with two upward thrusters is on the ground, and only one of them fires, the rocket's center of mass with accelerate upward, but also the rocket will experience a moment about its center of mass. The current commit can solve for rotational acceleration due to a moment, but not the acceleration due to a force acting somewhere other than the center of mass. The next commit should include some verified approach to simulating this case.