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 ...

, analytical dynamics, also known as classical dynamics or simply dynamics, is concerned with the relationship between

motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and mea ...

of bodies and its causes, namely the

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

s acting on the bodies and the properties of the bodies, particularly

mass Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...

and

moment of inertia The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceler ...

. The foundation of modern-day dynamics is

Newtonian mechanics Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in motion ...

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-Lou ...

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) ''momenta ...

History

The field has a long and important history, as remarked by

Hamilton Hamilton may refer to: People * Hamilton (name), a common British surname and occasional given name, usually of Scottish origin, including a list of persons with the surname ** The Duke of Hamilton, the premier peer of Scotland ** Lord Hamilt ...

: "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 Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...

, and especially since the wonderful extension which was given to that science by

Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * 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 In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...

within classical dynamics.

Relationship to statics, kinetics, and kinematics

Historically, there were three branches of

: *"

statics Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...

" (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 ki ...

" (the study of motion and its relation to forces). *"

kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, Physical object, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause ...

" (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'' is a physics textbook based on some lectures by Richard Feynman, a Nobel laureate who has sometimes been called "The Great Explainer". The lectures were presented before undergraduate students at the Californ ...

''.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 Newton's laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows: # A body remains at rest, or in moti ...

Inertia Inertia is the idea that an object will continue its current motion until some force causes its speed or direction to change. The term is properly understood as shorthand for "the principle of inertia" as described by Newton in his first law ...

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 In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. If is an object's mass an ...

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 me ...

Newton's law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...

Special theory of relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...

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 func ...

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 In the physical science of dynamics, rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. The assumption that the bodies are ''rigid'' (i.e. they do not deform under the action of a ...

* Deformation mechanics *

Fluid dynamics 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) an ...

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 Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressible, flows are usually treated as being incompressible when the Mach number (the r ...

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 Statics is the branch of classical mechanics that is concerned with the analysis of force and torque (also called moment) acting on physical systems that do not experience an acceleration (''a''=0), but rather, are in static equilibrium with ...

References

{{Branches of physics Dynamics (mechanics) Classical mechanics