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There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
The configuration space and the phase space of the dynamical system both are Euclidean spaces, i. e. they are equipped with a Euclidean structure.The Euclidean structure of them is defined so that the kinetic energy of the single multidimensional particle with the unit mass = is equal to the sum of kinetic energies of the three-dimensional particles with the masses , …,:
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.
The concept of a dynamical system has its origins in Newtonian mechanics.There, as in other natural sciences and engineering disciplines, the evolution rule of dynamical systems is an implicit relation that gives the state of the system for only a short time into the future.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems .
Kinematics is a subfield of physics and mathematics, developed in classical mechanics, that describes the motion of points, bodies (objects), and systems of bodies (groups of objects) without considering the forces that cause them to move.
Conduction heat flux q k for ideal gas is derived with the gas kinetic theory or the Boltzmann transport equations, and the thermal conductivity is =, -, where u f 2 1/2 is the RMS (root mean square) thermal velocity (3k B T/m from the MB distribution function, m: atomic mass) and τ f-f is the relaxation time (or intercollision time period ...
In physics and engineering, kinetics is the branch of classical mechanics that is concerned with the relationship between the motion and its causes, specifically, forces and torques. [ 1 ] [ 2 ] [ 3 ] Since the mid-20th century, the term " dynamics " (or " analytical dynamics ") has largely superseded "kinetics" in physics textbooks, [ 4 ...