# Motion

Motion is the actualization of what potentially is. It refers to every kind of change, though common usage has the limited meaning of a change of place. 

There are as many kind of motion and of change as there are of being.  Some examples include translational motion (displacement), and vibrational motion (waves_).

# 1   Study

Calculus (from Latin calculus, literally "small pebble used for counting") is the mathematical study of change. It has two major branches: differential calculus (concerning rates of change and slopes of curves) and integral calculus.

These two branches are related to each other by the fundamental theory of calculus:

Newton called calculus the study of "fluxions," or units of change. (This is a more descriptive label for the field than "calculus" which simply means "calculating stone" and has been used to refer to a wide variety of areas of mathematics and logic).

# 2   Inertia

Inertia is the resistance of any physical object to any change in its state of motion.

# 3   History

Aristotle first discussed the concept of motion in Physics. Aristotle defined motion as the fulfillment, insofar as it exists of potentially, of that which exists potentially.  He found, as he said, as many types of motion as there are meanings of the word "is". 

Motion remained puzzling for over two millenia until Newton Enunciated his laws. Newton's laws brought about a scientific and philosophical revolution. Using them, Laplace reduced the solar system to an explicable machine. They have formed the basis of aviation and rocketry. 

Edmund Halley (1656-1742) found Newton's mathematics so complex that he had to ask Newton for help several times, eventually prompting Newton to write out his theory in full, which became the Principia.

Newton presented his laws of motion in 1687 in a book titled Philosophiæ Naturalis Principia Mathematic ("Mathematics of `Natural Philosophy`_"). Despite being famous for the invention of calculus, Newton's magnum opus is written in the language of geometry probably because Newton felt it would be too much to introduce a major new theory in a totally new language. Many of the proofs in the book Newton had in fact originally discovered via calculus, he simply translated them back into geometry.

Newton and Leibniz invented calculus at roughly the same time independently of each other, because they both were trying to find a solution to the same problem.

Newton left some of assumptions unexamined. However, his method were so successful that it was not until two hundred years later that the foundations of Newtonian mechanics were carefully examined, principally by the Viennese physicist Ernst Mach_. 

Newtonian mechanics breaks down for systems moving with a speed comparable to the speed of light and also for systems of atomic dimensions or smaller where quantum effects are significant.  The failure arises become of limitations to the classical concept of space, time, and the nature of measurement.

The terms Newtonian mechanics and classical physics are often used interchangeably except that classical physics is taken to include Maxwell's theory of electromagnetism. The term "modern physics" typically describes developments in physics after relativity_ and `quantum mechanics`_ appeared on the scene. 

Newton's laws of motions are by no means self-evident. According to Aristotle, the natural state of bodies is rest: bodies move only when a force is applied. Aristotelian mechanics was accepted for two thousand years because it seemed intuitively correct. 

There are alternatives approaches to the Newtonian formulation of mechanics. Among these are the formulations of Lagrange and Hamilton, which take energy rather than force as the fundamental concept. However, these formulations are physically equivalent to Newtonian physics.