Dynamics (mechanics)

In physics, dynamics or classical dynamics^[1]^[2]^[3] is the study of forces and their effect on motion. It is a branch of classical mechanics, along with statics and kinematics. The fundamental principle of dynamics is linked to Newton's second law.^[4]

Subdivisions

Rigid bodies

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 applied forces) simplifies analysis, by reducing the parameters that describe the configuration of the system to the translation and rotation of reference frames attached to each body.^[5]^[6] This excludes bodies that display fluid, highly elastic, and plastic behavior.

The dynamics of a rigid body system is described by the laws of kinematics and by the application of Newton's second law (kinetics) or their derivative form, Lagrangian mechanics. The solution of these equations of motion provides a description of the position, the motion and the acceleration of the individual components of the system, and overall the system itself, as a function of time. The formulation and solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems.

Fluids

In physics, physical chemistry 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 hydrodynamics (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation.

Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.

Before the twentieth century, "hydrodynamics" was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, both of which can also be applied to gases.^[7]

Applications

Classical dynamics finds many applications:

Aerodynamics, the study of the motion of air
Brownian dynamics, the occurrence of Langevin dynamics in the motion of particles in solution
File dynamics, stochastic motion of particles in a channel
Flight dynamics, the science of aircraft and spacecraft design
Molecular dynamics, the study of motion on the molecular level
Langevin dynamics, a mathematical model for stochastic dynamics
Orbital dynamics, the study of the motion of rockets and spacecraft
Stellar dynamics, a description of the collective motion of stars
Vehicle dynamics, the study of vehicles in motion

Generalizations

Non-classical dynamics include:

System dynamics, the study of the behavior of complex systems
Quantum chromodynamics, a theory of the strong interaction (color force)
Quantum electrodynamics, a description of how matter and light interact
Relativistic dynamics, a combination of relativistic and quantum concepts
Thermodynamics, the study of the relationships between heat and mechanical energy

References

^ Greenwood, D.T. (1997). Classical Dynamics. Dover books on mathematics. Dover Publications. ISBN 978-0-486-69690-4. Retrieved 2025-02-23.
^ Thornton, S.T.; Marion, J.B. (2004). Classical Dynamics of Particles and Systems. Brooks/Cole. ISBN 978-0-534-40896-1. Retrieved 2025-02-23.
^ José, J.V.; Saletan, E.J. (1998). Classical Dynamics: A Contemporary Approach. Cambridge University Press. ISBN 978-0-521-63636-0. Retrieved 2025-02-23.
^ Mittelstedt, Christian (2025). "Kinetics of a point mass". Engineering Mechanics 3: Dynamics. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 35–69. doi:10.1007/978-3-662-69973-7_2. ISBN 978-3-662-69972-0.
^ B. Paul, Kinematics and Dynamics of Planar Machinery, Prentice-Hall, NJ, 1979
^ L. W. Tsai, Robot Analysis: The mechanics of serial and parallel manipulators, John-Wiley, NY, 1999.
^ Eckert, Michael (2006). The Dawn of Fluid Dynamics: A Discipline Between Science and Technology. Wiley. p. ix. ISBN 3-527-40513-5.

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[1] Greenwood, D.T. (1997). Classical Dynamics. Dover books on mathematics. Dover Publications. ISBN 978-0-486-69690-4. Retrieved 2025-02-23.

[2] Thornton, S.T.; Marion, J.B. (2004). Classical Dynamics of Particles and Systems. Brooks/Cole. ISBN 978-0-534-40896-1. Retrieved 2025-02-23.

[3] José, J.V.; Saletan, E.J. (1998). Classical Dynamics: A Contemporary Approach. Cambridge University Press. ISBN 978-0-521-63636-0. Retrieved 2025-02-23.

[z988-4] Mittelstedt, Christian (2025). "Kinetics of a point mass". Engineering Mechanics 3: Dynamics. Berlin, Heidelberg: Springer Berlin Heidelberg. pp. 35–69. doi:10.1007/978-3-662-69973-7_2. ISBN 978-3-662-69972-0.

[5] B. Paul, Kinematics and Dynamics of Planar Machinery, Prentice-Hall, NJ, 1979

[6] L. W. Tsai, Robot Analysis: The mechanics of serial and parallel manipulators, John-Wiley, NY, 1999.

[7] Eckert, Michael (2006). The Dawn of Fluid Dynamics: A Discipline Between Science and Technology. Wiley. p. ix. ISBN 3-527-40513-5.

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