Equations of motion modification consistent with conservation of momentum, see variable-mass system. It may be simple to write down the equations of motion in vector form using Newton's laws of motion, but the components may vary in complicated ways with spatial coordinates and time, and solving them is not easy. Often there is an excess of variables to solve for the problem completely, so Newton's laws are not always the most efficient way to determine the motion of a system. In simple cases of rectangular geometry, Newton's laws work fine in Cartesian coordinates, but in other coordinate systems can become dramatically complex. The
Elements of the Philosophy of Newton mutual Action of Bodies upon Light. Of the Resemblance between the seven Primitive Colours and the seven Notes in Musick. Introductory Ideas concerning Gravity and the Laws of Attraction: That the Opinion of a subtil Matter, Vortices, and a Plenitude, ought to be rejected (But not that subtile Aether which Sir Isaac makes the Cause of Attraction, Refraction, Animal Motion, &c. which pervades the Universe). That the Vortices and Plenitude of Descartes are impossible, and consequently that there is some other Cause of Gravity. What is meant by Vacuity and Space, without which there could be neither Gravity nor Motion.