Motion (physics)

As a movement in the physical sense is defined as the change in the place of an observed object with time.

The two disciplines of physics that deal with the movement as a movement teaching are:

• The kinematics and teaching of the description of motion
• The dynamics ( in engineering mechanics: the kinetics ) as the theory of the causes of motion

• 5.1 Equations of Motion
• 5.2 Chaotic motion

• 6.1 Motion of Rigid Bodies
• 6.2 Statistical View of movement
• 6.3 motion of liquids and gases

Movement and train

The totality of all the places where a point-like object in the course of a movement, called trajectory or trajectory. Trajectories are always continuous ( ie continuous in the mathematical sense ) and, if the motion at any point of the trajectory comes to a standstill, even smooth ( ie differentiable in the mathematical sense ). If at any time the place known, refers to the function as a path-time law of motion.

Relativity of motion

The description of the motion of an observed object depends on the observer. A person in the passenger seat of a moving car appears, for example, from the perspective of a pedestrian moving at the roadside while they seem to rest from the driver's perspective. Another example: In the view of the sun, the author of this text moves at high speed on a nearly circular orbit around the sun and moves at the same time, also at high speed in a circle around the earth's axis. From the perspective of the reader but the author seems to stand still.

Speed ​​and acceleration

The velocity is the ratio of the length of a small, at least approximately, straight piece of the trajectory to the time it takes the object to traverse this stretch. The smaller the stretch, the more accurately can be a time and place to assign a specific instantaneous velocity. The velocity has a direction corresponding to the direction of movement at the time. The velocity is a vector which is tangent to the trajectory at the relevant point.

As they proceed on the path curve, the speed can change the one hand, its amount and on the other hand their direction. What is referred to in slang depending on the situation as acceleration, braking or cornering, ie in physics and engineering uniform acceleration. Acceleration is defined as the ratio of change of the velocity vector to the time period in which the change takes place. In tangential changes only the magnitude of the speed at only the normal acceleration direction. In the general case the vector sum results from tangential acceleration and normal acceleration the acceleration vector.

Mathematically, the path-time law of a point-like object, which is the position vector, a continuous function of time. Is it also differentiable, the first derivative of the velocity vector, the second derivative is the acceleration vector.

Special forms of the movement of individual objects

Uniform rectilinear motion

Of rectilinear uniform motion is when the trajectory is a straight line portion, and the velocity at each point of the path is the same. A uniform rectilinear motion is occurring exactly when the acceleration is zero everywhere.

Uniformly accelerated motion

With a uniformly accelerated motion, the acceleration of the same magnitude and the same direction at each point of the trajectory. The trajectory of a uniformly accelerated motion is either a line segment or a parabola.

Circular motion

In a circular movement, the trajectory is circular. If, in a circular motion of the magnitude of the velocity is the same everywhere, then it is the uniform circular motion, having a zero tangential acceleration and normal acceleration is directed to the circle center.

Periodic motion

For a periodic motion the object under observation after a certain time, the period versa, back to the starting point and back it has the same direction and the same speed. Periodic movements have closed trajectories. The circular movement is a special case of a periodic motion.

Harmonic oscillation

Another example of a periodic motion of the harmonic oscillation, at which the change of the location in time follows a sine function. A classic example of a harmonically oscillating object is a spring pendulum. In general, each object oscillates harmoniously which is slightly displaced from an equilibrium position. Fourier analysis is any periodic movement can be represented as the sum of harmonics whose frequencies are integer multiples of the fundamental frequency, the inverse of the period duration.

Ergodic movement

In an ergodic motion the trajectory fills a space cut evenly.

Dynamics

A straight - uniform motion of a point-like object is made after it is once set in motion, without further intervention unchanged ever-advancing ( inertia principle of mechanics). For all the changes the action of a force is blamed. This is also the basic definition of force in physics and engineering.

Equations of motion

A movement equation is a differential equation whose solution is the path-time law. Equations of motion are ordinary differential equations of second order in time. The fundamental equation of mechanics establishes a relationship between the applied force and the second derivative of the distance-time law. By determining the position and velocity at a given time as initial conditions the further time evolution is uniquely determined. In other words, one knows all the attacking forces, so you can - starting from the initial conditions - predict or calculate back the movement of the object.

Chaotic motion

From a chaotic motion occurs when the equation of motion is such that small changes in the initial conditions large changes in the resulting movement have resulted.

Movement of several objects

Motion of rigid bodies

The motion of a rigid body can be in the movement of the center of gravity ( translation) and rotation movements of the body about axes passing through the center of gravity, disassemble. The equations of motion for the rotation called Euler equations. Robust rotary movements arise only those axes with respect to which the moment of inertia of the body minimum or maximum.

Statistical View of movement

The movements of a large number of similar objects, such as the molecules of a gas, to describe statistically. It is defined as the totality of all possible states of motion of all objects that are compatible with the measured state variables (eg, energy, volume and number of particles ), as an ensemble. It is postulated then, that all possible states of motion are equally probable and derives statements about the probability distributions of the physical quantities from. The Maxwell - Boltzmann distribution are, for example, the ( probability ) distribution of the amount of particle velocities in an ideal gas.

Movement of liquids and gases

The motion of deformable bodies ( especially liquids and gases) can no longer describe a few orbits by some.

Depending on the type of movement are distinguished in the following cases:

• Stationary flow: The flow pattern is constant over time.
• Laminar flow: The fluid can be decomposed into individual flow filaments that do not mix.
• Turbulent flow: The flow is neither stationary nor laminar. It occurs in all scales turbulence.

For the characterization of a flow, the Reynolds number will help.

The equations of motion of liquids and gases, the Navier-Stokes equations. They are derived from the basic equation of mechanics.

Movement on a microscopic scale

The concept of point-like particles that move with well-defined velocities on a path curve, is in truth a model that is sustainable only a certain size of the scale. The model of the trajectory, for example, fails during the movement of electrons in an atom of the conduction electrons in a metal of protons and neutrons in the nucleus, or photons.

To analyze these situations, you have to precise representation of quantum mechanics, passing over, in describing physical objects by a wave function. From the wave function, one can derive the probability with which an object is located at a certain place or a certain speed has. The Heisenberg uncertainty principle this limits the accuracy of a simultaneous measurement of position and velocity; also is the effect of each measure on the wave function and changed the future time evolution of the probabilities.