Newton laws are linear ? Big if true! Newton's law of gravitation (an application of second law) is highly nonlinear. In fact, it is SO nonlinear it led to creation of the field nonlinear dynamics, concept of chaos, and dynamical systems theory (via the three-body problem of Poincare).
A mass moving in 1D under a potential V(x) has the equation md^2x/dt^2=-dV/dx via second law, so if V is anything other than linear or quadratic in x, this is nonlinear ODE of x. But if you mean linearity between force and acceleration, then it is linear.
At the scale of a controlled system like the Apollo Lunar Lander, all potentials are close enough to quadratic that you can just stuff the difference in the noise term.
Newton laws are linear ? Big if true! Newton's law of gravitation (an application of second law) is highly nonlinear. In fact, it is SO nonlinear it led to creation of the field nonlinear dynamics, concept of chaos, and dynamical systems theory (via the three-body problem of Poincare).
Newton's laws of motion, not Newton's law of gravitation.
A mass moving in 1D under a potential V(x) has the equation md^2x/dt^2=-dV/dx via second law, so if V is anything other than linear or quadratic in x, this is nonlinear ODE of x. But if you mean linearity between force and acceleration, then it is linear.
At the scale of a controlled system like the Apollo Lunar Lander, all potentials are close enough to quadratic that you can just stuff the difference in the noise term.