What is Degrees of freedom: Definition and 174 Discussions

In various scientific fields, the word freedom is used to describe the limits to which physical movement or other physical processes are possible. This relates to the philosophical concept to the extent that people may be considered to have as much freedom as they are physically able to exercise. The number of independent variables or parameters for a system is described as its number of degrees of freedom. For example the movement of a vehicle along a road has two degrees of freedom; to go fast or slow, or to change direction by turning left or right. The movement of a ship sailing on the waves has four degrees of freedom since it can also pitch nose-to-tail and roll side-to-side. An aeroplane can also climb and sideslip, giving it six degrees of freedom.
Degrees of freedom in mechanics describes the number of independent motions that are allowed to a body, or, in case of a mechanism made of several bodies, the number of possible independent relative motions between the pieces of the mechanism. In the study of complex motor control, there may be so many degrees of freedom that a given action can be achieved in different ways by combining movements with different degrees of freedom. This issue is sometimes called the degrees of freedom problem.
In mathematics, this notion is formalized as the dimension of a manifold or an algebraic variety. When degrees of freedom is used instead of dimension, this usually means that the manifold or variety that models the system is only implicitly defined.
See:

Degrees of freedom (mechanics), number of independent motions that are allowed to the body or, in case of a mechanism made of several bodies, number of possible independent relative motions between the pieces of the mechanism
Degrees of freedom (physics and chemistry), a term used in explaining dependence on parameters, or the dimensions of a phase space
Degrees of freedom (statistics), the number of values in the final calculation of a statistic that are free to vary
Degrees of freedom problem, the problem of controlling motor movement given abundant degrees of freedom

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  1. N

    Graviton bosonic degrees of freedom

    Hi, Could you pls advise me why in on-shell case graviton has two degrees of freedom? and in general how do I calculate bosonic or fermionic degrees of freedom of any particle? I was reading some books about supersummetry and stuck when they said gravitopn has two degrees of freedom and...
  2. D

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  3. V

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  4. S

    Statistics- Degrees of Freedom

    If I flip two coins at once and don't care which one is heads in the case of a head and a tail, how many degrees of freedom are there?
  5. S

    What are the two independent ratios used to specify a line's parameters?

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  6. I

    Thermodynamics & Degrees of Freedom

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  7. M

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  8. N

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  9. S

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  10. M

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  11. G

    Are Colour Degrees of Freedom Relevant in e+e- Annihilation Cross Section?

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  12. S

    Calculating Degrees of Freedom for Riemann Tensor in D Dimensions

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  13. G

    Are degrees of freedom in a molecule affected by phase change?

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  14. G

    Degrees of freedom - molecule of water vapor

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  15. L

    Functions that introduce new degrees of freedom?

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  16. H

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  17. marcus

    Spacetime-matter degrees of freedom in current LQG research

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  18. A

    How many degrees of freedom does angular momentum have?

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  19. S

    Physics degrees of freedom problem

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  20. M

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  21. P

    Calculate Degrees of Freedom for 10 cc Oxygen Gas at STP

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  22. E

    Quantum Fields as having infinite degrees of freedom?

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  23. M

    Zero degrees of freedom. Does it has any sense?

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  24. Jimmy

    Dimensions and Degrees of Freedom

    When considering the three dimensions of space and our freedom of movement in that space, does our ability to change our state of motion (acceleration) imply an existence of a fourth dimension, ie. four space-time dimensions? Given three dimensions each mutually perpendicular, we can move...
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