VTOL Hover Balance 2D: Planar Rigid-Body Thrust Vectoring

This is the 2D counterpart to the 3D VTOL hover-balance simulation, built as an independent planar rigid-body model rather than a flattened version of the same scene. A jump-jet aircraft hovering on vectored thrust has no wings doing useful work at zero airspeed, so this model computes every newton of lift and every attitude-correcting torque directly from two real thrusters using explicit 2D cross-product mechanics (τ = r_x·F_y − r_y·F_x): a vectorable main nozzle below the center of gravity, and a nose-mounted reaction-control jet. Unlike the 3D engine's roll axis — an abstract torque coefficient with no accompanying reaction force — the nose RCS jet here contributes to both the rotational and translational equations of motion simultaneously, so trimming it both corrects pitch and nudges vertical velocity, exactly the momentum bookkeeping a real reaction-control thruster obeys. Throttle, nozzle angle, and RCS trim are full rigid-body controls, and switching on gusts forces you to actively counter random disturbance torques the way a real flight-control computer does many times a second.