By Dynamical Astronomy will be meant the connecting of mechanical and physical causes with observed phenomena. Formal Astronomy is so ancient that it is not possible to go back to its origin ; Dynamical Astronomy, on the other hand, did not begin until after the time of Aristotle, and then real advances were made at only very rare intervals.
Archimedes (287-212 B.C.), of Syracuse, is the author of the first sound ideas regarding mechanical laws. He stated correctly the principles of the lever and the meaning of the center of gravity of a body. The form and generality of his treatment were improved by Leonardo da Vinci (1452-1519) in his investigations of statical moments. The whole subject of Statics of a rigid body involves only the application of the proper mathematics to these principles.
It is a remarkable fact that no single important advance was made in the discovery of mechanical laws for nearly two thousand years after Archimedes, or until the time of Stevinus (1548-1620), who was the first, in 1586, to investigate the mechanics of the inclined plane, and of Galileo (1564-1642), who made the first important advance in Kinetics. Thus, the mechanical principles involved in the motions of bodies were not discovered until relatively modern times. The fundamental error in the speculations of most of the investigators was that they supposed that it required a continually acting force to keep a body in motion. They thought it was natural for a body to have a position rather than a state of motion. This is the opposite of the law of inertia (Newton’s first law). This law was discovered by Galileo quite incidentally in the study of the motion of bodies sliding down an inclined plane and out on a horizontal surface. Galileo took as his fundamental principle that the change of velocity, or acceleration, is determined by the forces which act upon the body. This contains nearly all of Newton’s first two laws. Galileo applied his principles with complete success to the discovery of the laws of falling bodies, and of the motion of projectiles. The value of his discoveries is such that he is justly considered to be the founder of Dynamics. He was the first to employ the pendulum for the measurement of time.
Huyghens (1629-1695), a Dutch mathematician and scientist, published his Horologium Oscillatorium in 1675, containing the theory of the determination of the intensity of the earth’s gravity from pendulum experiments, the theory of the center of oscillation, the theory of evolutes, and the theory of the cycloidal pendulum.
Newton (1642-1727) completed the formulation of the fundamental principles of Mechanics, and applied them with unparalleled success in the solution of mechanical and astronomical problems. He employed Geometry with such skill that his work has scarcely been added to by the use of his methods to the present day.
After Newton’s time, mathematicians soon turned to the more general and powerful methods of analysis. The subject of Analytical Mechanics was founded by Euler (1707-1783) in his work, Mechanica sive Motus Scientia (Petersburg, 1736) ; it was improved by Maclaurin (1698-1746) in his work, A Complete System of Fluxions (Edinburgh, 1742), and was highly perfected by Lagrange (1736-1813) in his Mecanique Analytique (Paris, 1788). The Mecanique Celeste of Laplace (1749-1827) put Celestial Mechanics on a correspondingly high plane.
For the fundamental principles of Mechanics consult :
For the theory of Relativity consult Das Relativitätsprincip, by M. Laue, and The Theory of Relativity, by R. D. Carmichael.
For velocity and acceleration and their resolution and composition consult :
For the history of Celestial Mechanics and Astronomy consult :