2010-11-20 00:59:02 8 Comments

I have noticed that authors in the literature sometimes divide characteristics of some phenomenon into "kinematics" and "dynamics".

I first encountered this in Jackson's E&M book, where, in section 7.3 of the third edition, he writes, on the reflection and refraction of waves at a plane interface:

- Kinematic properties: (a) Angle of reflection equals angle of incidence (b) Snell's law
- Dynamic properties (a) Intensities of reflected and refracted radiation (b) Phase changes and polarization

But this is by no means the only example. A quick Google search reveals "dynamic and kinematic viscosity," "kinematic and dynamic performance," "fully dynamic and kinematic voronoi diagrams," "kinematic and reduced-dynamic precise orbit determination," and many other occurrences of this distinction.

**What is the real distinction between kinematics and dynamics?**

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## 14 comments

## @starseed_trooper 2018-06-29 01:00:44

Primarily, the distinction between kinematics and dynamics is one of

causation. What do we mean by this? The etymology of the wordkinematicsis the Greekkinēma, which means motion. On the other hand, dynamics draws its origin fromdunamis, meaning power (though we are better off thinking of it as a power in potentia, as in the ability to do something).So? Well, we all know another word that is based of the Greek

kinēma--cinema. If we were to represent the trajectory of a particle as a function, as a computer simulation or as a movie, we would be providing a description of the particle's motion without explaining what caused it to move that way. But as physicists, we should not be merely content with painting a picture of a system's motion. That is the job for the artists.In order to explain why our system of interest exhibits the motion that we observe, we identify forces and potentials that may have been responsible for triggering the motion. In classical mechanics, once we have identified the forces and the initial conditions of the system (the dynamics), we can then solve a differential equation to obtain a solution parameterized in time (the kinematics).

The study of dynamical systems is, after all, a branch of mathematics. I hope this helps. Moreover, I hope that you appreciate that the distinction is not at all arbitrary, as some people have been led to think.

## @I am Back 2016-10-19 06:44:02

Mechanics can be broadly classified into following branches:

1.Statics- Deals with study of material objects at rest

ORdeals with the study of motion of objects under the effects of forces in equilibrium.Here time factor does not play any role.2.Kinematics- Deals with study of motion of material objects without taking into account the factors which causes motion( i.e. nature of force,nature of body).Here time factor plays an essential role.

3.Dynamics- Deals with study of motion of objects taking into account the factors which cause motion.Dynamics is based on concept of force.Here,time factor plays an essential role.

## @John Fistere 2016-05-31 22:40:21

In mechanical systems, I would say the difference is whether the forces involved are due to static or quasi-static situations in which the forces are due to weight/gravity, springs, etc. If the forces result from accelerations then we have a dynamic system, whereas the former would be a kinematic system.

In the transmission of light example of the original questioner, I don't understand the distinction that is being made. All of the phenomena are related to the interaction of particles and light which to my way of thinking is a dynamic system. But that's at a lower level.

## @Emilio Pisanty 2016-05-31 22:47:02

I disagree. Kinematics is, by etymology, the study of motion; restricting it to static situations is bizarre. I have yet to see either of those terms used in the literature in the senses you state, though maybe you can provide references.

## @Emilio Pisanty 2016-05-31 22:49:50

I'm also not sure how the second paragraph is at all an answer. In any case, the distinction drawn by Jackson makes perfect sense to me: Snell's law is required simply to have a wave on one side match up with a wave on the other side with matching phases along the boundary at all times even when their speeds are different; transmission and reflection coefficients, and their interaction with polarization, on the other hand, require the application of Maxwell's equations in their boundary form to know how the system will respond.

## @guillefix 2016-01-20 19:43:26

This is how I understand it. There is a series of definitions used in physics, and one used in engineering mostly. I'll describe the one used in physics first:

In

mechanics, wedescribethe motion of bodies, and thecausesthat effect them. This includes the special case where the "motion" is no motion, i.e. bodies are stationary.The description of the motion itself is called

kinematics. This just sets up the relevant degrees of freedom, represented as variables in a relevant mathematical form.The description of the causes, and how these causes effect the motion is called

dynamics. These causes are often divided into forces and torques. This description relates the variables describing the motion above, to forces, which should depend on those variables themselves. This means that in dynamics we often have closed equations that we can solve in full generality.Another division of the areas of classical mechanics, used mostly in engineering leaves the definition of kinematics the same, but what we referred to as dynamics above is called

kinetics.Dynamics then refers to mechanics applied to proper motion only (i.e. not including stationary case). In other words, dynamics is the kinematics and kinetics of proper motion.

Mechanics applied to the stationary case is referred to as

statics. In other words, statics is the kinematics and kinetics of static equilibrium.## @celtschk 2014-04-27 10:25:49

Another pragmatic definition: If you only need SI units derived from the meter and the second (length, time, velocity, acceleration, …), it's kinematics. If you also need SI units involving the kilogram (mass, energy, momentum, force, …), it's dynamics.

## @Chad Orzel 2010-11-20 01:27:43

In classical mechanics "kinematics" generally refers to the study of properties of motion-- position, velocity, acceleration, etc.-- without any consideration of why those quantities have the values they do. "Dynamics" means a study of the rules governing the interactions of these particles, which allow you to determine why the quantities have the values they do.

Thus, for example, problems involving motion with constant acceleration ("A car starts from rest and accelerates at 4m/s/s. How long does it take to cover 100m?") are classified as kinematics, while problems involving forces ("A 100g mass is attached to a spring with a spring constant of 10 N/m and hangs vertically from a support. How much does the spring stretch?") are classified as "dynamics."

That's kind of an operational definition, at least.

## @Matt Reece 2010-11-20 02:39:54

To try to make this a little sharper, I would say "kinematics" is about things that are determined by conservation laws: kinematics tells you that momentum and energy have to balance, for instance. "Dynamics" is any detail that depends on the interactions and not just on conserved quantities, and would tell you for instance the detailed cross-section of a scattering process as a function of the kinematically possible configurations.

## @Noldorin 2010-11-20 21:17:30

@Matt: That's not a standard definition however.

## @Rikki 2013-08-21 17:09:59

Kinematics:what Galileo worked on with his numerous experiments measuring displacement, velocity and acceleration of balls rolling down inclined plans.Dynamics:what Newton worked on when he formulated his three laws.## @Philip Gibbs - inactive 2012-01-09 19:25:38

Kinematics is about the range of movement or change a system can undergo, or the state space in which it acts. Dynamics is about the movement it undergoes according to the laws of motion.

For example the kinematics of a rigid body in space describes its possible coordinate positions and orientations and the range of velocities and angular velocities etc. The dynamics describes how these would change under the influence of a given system of forces.

This means that conservation of energy and other quantities is dynamical because it only holds when the equations of motion are in effect.

Although kinematics and dynamics are most used in classical mechanics you can extend the idea to quantum mechanics where the kinematics are described by the phase space and operators, while the dynamics is the evolution under the influence of a given Hamiltonian.

It is traditional to regard the distinction between kinematics and dynamics as absolutely clear cut, but possibly the most important thing to understand about them is that this is not always the case. As a simple example consider the case of a particle that can move along a fixed track. You could regard the constraint that keeps it on the track as kinematical and only its actual motion along the track would be part of the dynamics, but we know that at a deeper level the particle is held on the track by dynamical forces.

Another example might be conservation of charge. If you consider the Dirac equation for a charged particle in the presence of an electromagnetic field, you find that charge is conserved only under the influence of the equations of motion. If you quantise the system the charge is given by the sum of the quantised charges on the positrons and electrons which can only be created and destroyed in pairs. It is possible to view this as a kinematic constraint with the dynmaics only accounting for the motion of the particles.

Perhaps the best example is in electrodynamics where a vector potential describes the field kinematics with the electric and magnetic fields being given by suitable derivatives. In this case the Maxwell equation that tell us that the magnetic field has zero divergence is kinematical because it follows without use of the equations of motion, but the divergence of the electric field is equal to the electric current according to the equations of motion. So some of Maxwell's equations are kinematic and some are dynamic. In a deeper theory these fields may be derived from a system which exhibits electromagnetic duality where magnetic monopoles act as sources for the magnetic field. In that case the kinematic and dynamic parts of the Maxwell equation are interchanged under the duality so we are forced to realize that the original distinction between kinematic and dynamic was an illusion.

In the final analysis the evolution of the universe does not make the same distinction between kinematic and dynamic that physicists do and it is important to appreciate that at a deeper level kinematics may turn out to be dynamics or vice-versa. So any attempt to define the difference is to some extent arbitrary and may not stand the test of time.

## @Ron Maimon 2012-01-09 15:01:20

You should think of it in terms of programming a computer to simulate the physical system. Kinematics is the data structure you need to simulate the general situation, what variables with what range of values. Dynamics is the actual algorithm that simulates the motion.

## @lurscher 2011-01-26 16:30:57

I think in general, one might interpret a distinction between kinematical and dynamical models as loosely referring to phenomenological descriptions (kinematical) versus. descriptions obtained from first principles (dynamical)

## @ja72 2011-01-26 16:40:18

-1 : I disagree. Kinematic has to do with motions and paths but not with forces and masses. A kinematic description might tell you what are all the possible configurations, but a dynamic description will narrow it down to what is likely to happen in a time sequence.

## @Pavel Radzivilovsky 2010-11-30 21:03:01

The difference is:

consideration of forces.In many cases, forces themselves are related to location (lookup entries potential, potential energy, hamiltonian) so dynamics would allow you to predict system's behavior from given initial state.

## @Raskolnikov 2010-11-20 14:05:43

Since everybody already gave nice replies to this question, I'll give a more pragmatic answer:

Don't worry about it. It is an arbitrary distinction made by humans. Nature doesn't care if some phenomenon can be described/explained purely from kinematic considerations or not. It's not a fundamental distinction.

On the other hand, it is a useful distinction. I'm sure you know the distinction somehow implicitly when you solve problems.

Let me give an example in mechanics: you swing a pendulum in a vertical plane, you swing sufficiently fast so that the trajectory is a circle. What is the tension in the pendulum when it passes in the lowest point of the circle. The tension is a dynamical quantity, because it is a force. Now, when you solve the problem, you don't write down the full equation of Newton and solve them. You use the kinematic information you have about the trajectory: it's a circle, in the lowest part of the trajectory there is no tangential acceleration, so the acceleration is directed radially inwards and is $v^2/r$. From this you can find the tension by using purely kinematic considerations and never solving $\vec{F}=m\vec{a}$ as a differential equation.

I guess you understood that in physics we do this all the time. If we didn't, many problems would be impossible to tackle without resorting to extensive computer simulations all the time. In most problems we consider, we already have some idea of the kinematics, which permits to reduce the space of acceptable solutions. Sometimes so drastically (but that is only for the simplest problems) that we can solve them by purely kinematic considerations.

## @user566 2010-11-20 05:13:39

I'd say that kinematics has to do with the space of all possible configurations of a system at one time, for example what restrictions are placed on those by conservation laws. Dynamics has to do with how configurations change as a function of time. As always, the way the term is actually used may depend on the person.

## @ja72 2010-11-20 05:11:57

Statics: Study of forces in equilibrium without consideration of changes over time.Kinematics: Study of motions (position, velocity, acceleration)Kineto-statics: Study of forces in equilibrium, with the addition of motion related forces (like inertia forces via D'Alembert's principe) one instant at the time. Results from one time frame do not affect the results on the next time frame.Dynamics: Full consideration of time varying phenomena in the interaction between motions, forces and material properties. Typically there is an time-integration process where results from one time frame effect the results on the next time frame.As far as the source if kinematic and dynamic viscocity, I am not sure, and I have wondered this myself. Maybe it stems from the test methods used to measure each property.

## @Qmechanic 2012-01-09 15:29:53

It seems indeed natural to explain

staticswhen discussingdynamics.## @Griffin 2013-06-18 00:47:58

And these stem from

Mechanics:The study of interactions between bodies and forces that produce motion.