classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical m ...

, analytical dynamics, also known as classical dynamics or simply dynamics, is concerned with the relationship between motion of bodies and its causes, namely the forces acting on the bodies and the properties of the bodies, particularly mass and moment of inertia. The foundation of modern-day dynamics is Newtonian mechanics and its reformulation as

Lagrangian mechanics In physics, Lagrangian mechanics is a formulation of classical mechanics founded on the stationary-action principle (also known as the principle of least action). It was introduced by the Italian-French mathematician and astronomer Joseph-Lo ...

and

Hamiltonian mechanics Hamiltonian mechanics emerged in 1833 as a reformulation of Lagrangian mechanics. Introduced by Sir William Rowan Hamilton, Hamiltonian mechanics replaces (generalized) velocities \dot q^i used in Lagrangian mechanics with (generalized) ''moment ...

History

The field has a long and important history, as remarked by Hamilton: "The theoretical development of the laws of motion of bodies is a problem of such interest and importance that it has engaged the attention of all the eminent mathematicians since the invention of the dynamics as a mathematical science by Galileo, and especially since the wonderful extension which was given to that science by Newton." William Rowan Hamilton, 1834 (Transcribed in ''Classical Mechanics'' by J.R. Taylor, p. 237) Some authors (for example, Taylor (2005) and Greenwood (1997) ) include special relativity within classical dynamics.

Relationship to statics, kinetics, and kinematics

Historically, there were three branches of

: *" statics" (the study of equilibrium and its relation to forces) *"

kinetics Kinetics ( grc, κίνησις, , kinesis, ''movement'' or ''to move'') may refer to: Science and medicine * Kinetics (physics), the study of motion and its causes ** Rigid body kinetics, the study of the motion of rigid bodies * Chemical kin ...

" (the study of motion and its relation to forces). *" kinematics" (dealing with the implications of observed motions without regard for circumstances causing them). These three subjects have been connected to ''dynamics'' in several ways. One approach combined statics and kinetics under the name dynamics, which became the branch dealing with determination of the motion of bodies resulting from the action of specified forces; another approach separated statics, and combined kinetics and kinematics under the rubric dynamics. This approach is common in engineering books on mechanics, and is still in widespread use among mechanicians.

Fundamental importance in engineering, diminishing emphasis in physics

Today, ''dynamics'' and ''kinematics'' continue to be considered the two pillars of classical mechanics. Dynamics is still included in mechanical, aerospace, and other engineering curricula because of its importance in machine design, the design of land, sea, air and space vehicles and other applications. However, few modern physicists concern themselves with an independent treatment of "dynamics" or "kinematics," nevermind "statics" or "kinetics." Instead, the entire undifferentiated subject is referred to as ''classical mechanics''. In fact, many undergraduate and graduate text books since mid-20th century on "classical mechanics" lack chapters titled "dynamics" or "kinematics." In these books, although the word "dynamics" is used when acceleration is ascribed to a force, the word "kinetics" is never mentioned. However, clear exceptions exist. Prominent examples include '' The Feynman Lectures on Physics''.The Feynman Lectures on Physics Vol. I Ch. 9: Newton’s Laws of Dynamics
/ref> ;List of Fundamental Dynamics Principles * Newton's laws of motion ** Inertia **

Acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...

** Momentum **

Reaction Reaction may refer to a process or to a response to an action, event, or exposure: Physics and chemistry *Chemical reaction * Nuclear reaction *Reaction (physics), as defined by Newton's third law * Chain reaction (disambiguation). Biology and ...

* Newton's law of universal gravitation * Special theory of relativity

Axioms and mathematical treatments

Variational principle In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the values of quantities that depend on those funct ...

s and

Canonical transformation In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates that preserves the form of Hamilton's equations. This is sometimes known as form invariance. It need not preserve the form of the Hamiltonian itself. Canoni ...

s * Hamilton–Jacobi Theory

Related engineering branches

* Particle dynamics * Rigid body dynamics * Deformation mechanics * Fluid dynamics **

Hydrodynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and ...

** Gas dynamics **

Aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...

Related subjects

* Statics

References

{{Branches of physics Dynamics (mechanics) Classical mechanics