Analytical Mechanics on Superphysics

Dynamics

Wed, 18 Mar 2026 00:00:00 +0000

Dynamics is the science of accelerating or retarding forces and of the varied motions they must produce.

This science is entirely due to the moderns.

Galileo laid its first foundations.

The 4 Principles of Dynamics

Wed, 18 Mar 2026 00:00:00 +0000

If one conceives that the motion of a body and the forces soliciting it are decomposed according to three straight lines perpendicular to each other, one can consider separately the motions and forces relative to each of these three directions.

For, because of the perpendicularity of the directions, it is evident that each of these partial motions can be regarded as independent of the other two and that it can receive alteration only from the part of the force which acts in the direction of this motion; from which one can conclude that these three motions must follow, each individually, the laws of rectilinear motions accelerated or retarded by given forces.

Jacques Bernoulli

Wed, 18 Mar 2026 00:00:00 +0000

A thread, considered as an inflexible line without weight and without mass, being attached by one end to a fixed point and loaded, at the other end, with a small weight which can be regarded as reduced to a point, forms what is called a simple pendulum;

The law of vibrations of this pendulum depends uniquely on its length, that is to say on the distance between the weight and the point of suspension.

Daniel Bernoulli; Inertia

Wed, 18 Mar 2026 00:00:00 +0000

d’Alembert’s Treatise on Dynamics of 1743, put an end to these challenges by offering a direct method for solving, or at least for putting into equations, all the problems of Dynamics.

It reduces all the laws of motion of bodies to those of their equilibrium and thus brings Dynamics back to Statics.

General Formula Of Dynamics For The Motion Of A System Of Bodies Animated By Any Forces

Wed, 18 Mar 2026 00:00:00 +0000

When the forces acting on a system of bodies are arranged in accordance with the laws set forth in the first Part of this Treatise, these forces destroy each other mutually and the system remains in equilibrium.

But, when equilibrium does not take place, the bodies must necessarily move, obeying wholly or in part the action of the forces soliciting them. The determination of the motions produced by given forces is the object of this second Part.