1100-1138 - Avempace develops the concept of a reaction force
1100-1165 - Hibat Allah Abu'l-Barakat al-Baghdaadi discovers that force is proportional to acceleration rather than speed, a fundamental law in classical mechanics
1121 - Al-Khazini publishes The Book of the Balance of Wisdom, in which he develops the concepts of gravitational potential energy and gravity at-a-distance
1589 - Galileo Galilei uses balls rolling on inclined planes to show that different weights fall with the same acceleration
1638 - Galileo Galilei publishes Dialogues Concerning Two New Sciences
1658 - Christiaan Huygens experimentally discovers that balls placed anywhere inside an inverted cycloid reach the lowest point of the cycloid in the same time and thereby experimentally shows that the cycloid is the tautochrone
1668 - John Wallis suggests the law of conservation of momentum
1733 - Daniel Bernoulli derives the fundamental frequency and harmonics of a hanging chain by solving an ordinary differential equation
1734 - Daniel Bernoulli solves the ordinary differential equation for the vibrations of an elastic bar clamped at one end
1738 - Daniel Bernoulli examines fluid flow in Hydrodynamica
1739 - Leonhard Euler solves the ordinary differential equation for a forced harmonic oscillator and notices the resonance phenomenon
1742 - Colin Maclaurin discovers his uniformly rotating self-gravitating spheroids
1743 - Jean le Rond d'Alembert publishes his "Traite de Dynamique", in which he introduces the concept of generalized forces for accelerating systems and systems with constraints
1747 - Pierre Louis Maupertuis applies minimum principles to mechanics
1759 - Leonhard Euler solves the partial differential equation for the vibration of a rectangular drum
1764 - Leonhard Euler examines the partial differential equation for the vibration of a circular drum and finds one of the Bessel function solutions
1788 - Joseph Louis Lagrange presents Lagrange's equations of motion in Mécanique Analytique
1789 - Antoine Lavoisier states the law of conservation of mass
1813 - Peter Ewart supports the idea of the conservation of energy in his paper On the measure of moving force
1821 - William Hamilton begins his analysis of Hamilton's characteristic function
1834 - Carl Jacobi discovers his uniformly rotating self-gravitating ellipsoids
1834 - John Russell observes a nondecaying solitary water wave (soliton) in the Union Canal near Edinburgh and uses a water tank to study the dependence of solitary water wave velocities on wave amplitude and water depth
1835 - William Hamilton states Hamilton's canonical equations of motion
1835 - Gaspard Coriolis examines theoretically the mechanical efficiency of waterwheels, and deduces the Coriolis effect.
1841 - Julius Robert von Mayer, an amateur scientist, writes a paper on the conservation of energy but his lack of academic training leads to its rejection.
1842 - Christian Doppler proposes the Doppler effect