What is Degree of freedom: Definition and 68 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.

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

View More On Wikipedia.org
  1. V

    B Conflicting definition of degree of freedom in Kinetic Theory of Gases

    I am seeing conflicting definitions of degree of freedom in my textbook. If I look at the definition given as per screenshot below then it is the number of independent terms/variables/coordinates used to define the energy of a molecule. But, if I look at the statement of Equipartition of energy...
  2. Z

    A Order of rotations due to torque in 3DOF in simulations

    Hi, I am running a computational fluid dynamics (CFD) simulation. Supposed I have a symmetrical rigid body in space experiencing torque in the global x,y,z axes. It is stationary at t = 0. I also constrain it to only allow rotations in 3DOFs, and no translation. It will rotate and I need to...
  3. LCSphysicist

    Degree of Freedom: Definition & Examples - Confused? Ask Here!

    Hello. I am a little confused with the definition of degree of freedom, since i always count it wrong when it is necessary: Is it the number of coord?inates necessary to describe the problem, or the number of independent coordinates I ask this because, for example, see this problem: A rotator...
  4. curiousPep

    I Lagrangian mechanics - generalised coordinates question

    I think I undeerstand Lagrangian mechanics but I have a question that will help to clarify some concepts. Imagine I throw a pencil. For that I have 5 generalised coordinates (x,y,z and 2 rotational). When I express Kinetic Energy (T) as: $$T = 1/2m\dot{x^{2}}+1/2m\dot{y^{2}}+1/2m\dot{z^{2}} +...
  5. L

    I Physical parameters for spin 1/2 particles

    I am having trouble to understand what it means by "physically relevant real parameters" and how does it help us to specify a quantum system. Let say, we have a state of k half spin electrons? My guess is about the local phase of the spin, and this would make it 2^k parameters since each...
  6. C

    Single degree of freedom system/equivalent mass

    It's possible to use Comsol to model a simple truss and the resulting frequency response looks like a single degree of freedom system. Using that data you can calculate a value for the spring constant, damping, and equivalent mass of the system etc and plot the frequency response of an ideal...
  7. A

    MHB Degree of Freedom: Maths Definition & Differential Equations

    what is meant by the degree of freedom in Mathematics? Especially in the differential equations.
  8. binbagsss

    Propagating degree of freedom (GR)

    Homework Statement I am trying to follow my lecture notes, attached below, an argument to the number of degrees of freedom from the number of constraints of he Einstein field equations The bit I a man stuck on is the second thumbnail, and the deduction that he righ hand side of 5.18 only has...
  9. Death eater

    When boiling water, what is the degree of freedom inside the vapour dome?

    When water converts to steam while boiling a vapour dome can be formed, what is the degree of freedom inside this vapour dome and on the saturated points?
  10. O

    2 degree of freedom system modeling

    Hello, I'm having difficulty finding equation of motion for 3 degree of freedom spring mass system. Homework Statement the positions of the masses at the equilibre are respectively X10, X20, X30 At t = 0s, the mass m1 is drawn to the...
  11. Killtech

    B Is the speed of light a degree of freedom?

    The speed of light is postulated to be constant in all inertial frames. but why is it called a postulate actually? looking at the SI definition of the meter that is specifically defined by the propagation of light i notice it makes it constant by definition. so isn't this actually just a choice...
  12. F

    Counting degrees of freedom in field theory

    I'm having a bit of trouble with counting the number of physical ("propagating") degrees of freedom (dof) in field theories. In particular I've been looking at general relativity (GR) and classical electromagnetism (EM). Starting with EM: Naively, given the 4-potential ##A^{\mu}## has four...
  13. Sanchayan Ghosh

    Understanding the four bar linkage DOF

    Hello guys, I have a doubt with understanding DOFs. I have taken the example of the four bar linkage. According to Grueblr's condition, the DOF of this mechanism is 1. \mbox{DOF} = 3(l-1) + 2j_1 + 2j_2\\l=4\ j_1=4\ j_2=0\\\mbox{DOF} = 1 In the above figure, the links next to the ground link...
  14. S

    A ?Gravity in 3D: Computing Degree of Freedom

    Dear all can anyone help me to understand why gravity in 3 dim doesn't have local degree of freedom. How can i compute the degree of freedoms for gravity in and dimension D. If i consider massless gravity in 3d is the graviton propagating
  15. M

    Degrees of freedom of harmonic oscillator

    Homework Statement A three-dimensional harmonic oscillator is in thermal equilibrium with a temperature reservoir at temperature T. The average total energy of oscillator is A. ½kT B. kT C. ³⁄₂kT D. 3kT E. 6kT Homework Equations Equipartition theorem The Attempt at a Solution So I know the...
  16. Y

    Mechanics, degree of freedom question

    Homework Statement Calculate the DoF (mobility) of the following system: Homework Equations [/B] M = 3(L-1) - 2J1 - J2 (where L = number of links, J1 is the number of full binary joints and J2 is the number of half joints. The Attempt at a Solution I am very confident about there being...
  17. W

    ChemE. Degree of Freedom analysis & recycled stream

    Homework Statement The problem want me to do a degree of freedom analysis on the following process using the information provided. There are two chemical rx in the process. The desired production rate of DEA (D) is 105,000 kg/h. The air composition is 21% mol% O2 and 79 mol% N2[/SUB. 25% of...
  18. Spacexplorer

    Understanding How Dampers and Springs Work in Car Suspension Systems

    Hi guys. It could be an easy question but I started at the deepest. I wonder how it works like a car suspension system. How does damper work with spring? What is the difference between forced-nonforced systems? Why do we calculate frequency of spring? What does it provide us? What is the point...
  19. A

    Interpreting Kinetic Temperature for Solids / Liquids

    Hi all, I'm brushing up on some thermodynamics, and having been reading up on the interpretation of temperature as derived from kinetic theory. I can follow the derivation for an ideal, monatomic gas which relates temperature to the average, translational kinetic energy of the molecules. Most...
  20. Benevito

    What are Valley Degrees of Freedom in Semiconductor Bands?

    Could someone please explain what valley degrees of freedom are?
  21. S

    Degree of freedom of gravitino

    Please tell me how to count the degree of freedom of gravitino on the mass-shell? I read http://arxiv.org/abs/1112.3502, but I can't understand it. How about supervielbein?
  22. S

    "degree of freedom" (singular)?

    Is it common terminology to refer to a state variable as a "degree of freedom"? From the current Wikipedia article on degrees of freedom : https://en.wikipedia.org/wiki/Degrees_of_freedom_(physics_and_chemistry) Edit: Another example of using "degrees of freedom" to mean a set of variables...
  23. T

    Mechanical Vibration: 3 Degree of Freedom

    Homework Statement http://i.imgur.com/wJu0AEs.jpg http://i.imgur.com/J9sEWgq.jpg?1 Homework Equations Kinetic Energy = T = 1/2 * I * (theta_dot)^2 Potential Energy = V = 1/2 * Kt * theta^2 The Attempt at a Solution Matlab Code and Results: >> I1=3600; I2=200; I3=800; I4=4800; d1=0.15...
  24. S

    Degree of freedom of a block of wood sliding on a horizontal plane

    Homework Statement Find out the degrees of freedom of a block of wood sliding on a horizontal plane. Homework Equations DoF=Nn-k N=no. of dimensions. n=no. of particles.k= no. of constraints. The Attempt at a Solution I am considering the block of wood as a rigid body made of n no. of...
  25. G

    CHI square test - finding degree of freedom

    Homework Statement i have problem of finding the degree f freedom for this question. the ans for v is 3 , but my ans is v=n-1 , where n = 6 , so my v=5... Homework EquationsThe Attempt at a Solution
  26. Hardik Batra

    Why does CO molecule have 7 degrees of freedom?

    In my book showed that degree of freedom of CO(carbon monoxide) molecule is 7... I think... 3 degree of freedom for translation motion and 2 degree of freedom for rotational motion. then total degree of freedom is 3 + 2 = 5. But how it is 7 ?
  27. N

    Degree of freedom and formula for standard variation

    For a set with n points of data, why is the "degree of freedom" of the standard variance n-1? Hell, what does "degree of freedom" actually mean? Heck, my book "proves" this by saying that since ##\sum_1^n (x_i - \bar{x}) = 0## (obviously), then ##\sum_1^n (x_i - \bar{x})^2## must have n-1...
  28. R

    [spring system] 3 degree of freedom system and its properties

    Hello, I was given the attached 3 degree of freedom spring system with the purpose of analyzing it. I came up with the following equation of motion and then I ran Matlab to calculate the corresponding natural frequencies and mode shapes using eigenvalues and eigenvectors; I was asked to...
  29. U

    Degree of Freedom (Kutzbach Criterion)

    Homework Statement To figure out the degree of freedom of a mechanism in 3D space. The resulting diagram is in the attachment. It consists of 6 revolute joints and 1 prismatic joint. All joints act in the z-x plane besides joint 1 which revolves around the z axis (i.e moves the mechanism into...
  30. H

    What exactly does a degree of freedom mean?

    I have seen this word used in every context, is there a solid definition??
  31. H

    Finite amount of degree of freedom for entropy available in universe (?)

    The spectrum of the Cosmic Microwave Background radiation - the flash of the Big Bang, aligns almost precisely with the shape of the Black Body radiation curve. This means that the CMB radiation came from a state that was in thermal equilibrium. Since thermal equilibrium is a state of maximum...
  32. H

    Specific Heat: Degree of Freedom & Energy Storage

    Homework Statement Okay I have to write an EEI (Extended Experimental Investigation) for physics in relation to which radiator coolant is best from a thermodynamics point of view, thus the specific heat of the coolant is the main focus. But to incorporate more depth into the report, I was going...
  33. S

    Impulse for 2 Degree of freedom system

    I have a question which might be simple. Suppose we have a 2 degree of freedom system such as a double pendulum which is suspended from the ceiling. Now if the second ball (the lower one) collides with the wall, how can we find the impulse exerted on the ball. I mean do we consider the...
  34. S

    Multi Degree of Freedom system (Structural Dynamics)

    I have been reading the theory/math concerning the solution of multi degree of system-free and forced vibration. I need to do this for an upcoming project which is to do with some development concerning vibrations and thus thought that I should see again over my Engineering school notes...
  35. P

    Is the angular degree of freedom on a circle considered a gauge degree?

    Is it okay to classify the angular degree of freedom of a point on a circle as a gauge degree of freedom? (i). One can add 2Pi to angle without changing the position of point. (ii). U(1) symmetry exp (i theta)
  36. T

    Who can tell me something about degree of freedom in statistic?

    being stuck by standard deviation, I just can't understand the difference between n and n-1. who can give me some concrete examples? thank you!
  37. T

    Mystery of the lost degree of freedom in a gauge theory

    Something is totally not making sense. In a complex scalar field theory, I have two field degrees of freedom, which I parametrize in polar field coordinates: \phi = \rho e^{i\theta}/\sqrt{2}, where \rho and \theta are real-valued; and its Lagrangian takes the form: \mathcal{L} =...
  38. A

    Single Degree of Freedom Equation of Motion(Newtons Second Law)

    Homework Statement Hello guys. Really need your helps. When I construct an equation(moment about point O), do I have to include the rod's mass also? I've heard that I can neglect the rod's mass due to equilibrium equation. On the other hand, I've also heard that I can only neglect mass if the...
  39. S

    Linear degree of freedom - Equipartition theorem

    Homework Statement Consider a classical 'degree of freedom' that is linear rather than quadratic: E = c|q| for some constant c. Derive the equipartition theorem using this energy and show that the average energy is Ebar = kT. Homework Equations Z = \sum e^{-\beta E(q)} = \sum...
  40. B

    2 degree of freedom mass spring damper system

    For a project we are supposed to design the suspension system of a half car model. We are supposed to determine the values of the spring constants and damping constants. We are given the mass of the half car, the moment of inertia about the center of mass, and the wheel base. We are given a...
  41. D

    Natural frequency of large degree of freedom system

    I have a spring-mass system with 200 masses and 199 springs. All masses are 100 tonnes and stiffness 20 MN. The boundary conditions are fixed-free. I have constructed a lumped mass matrix and stiffness matrix and calculated the lowest natural frequency. Including the boundary conditions I...
  42. D

    What is the Degree of Freedom of a System?

    This is not really the homework. It is the university examination problem. The problem here is many teachers/professors answer differently and not much detailed. And we don't know who was the exact professor who create these problems. Homework Statement Instuction: Find the number of...
  43. O

    Mechanical system with two degree of freedom

    Homework Statement 1) Two cylinder can roll without sliding on a horizontal plan. they are connected throught the center by a spring of rigidity "k". They both share the same radius "R" and mass "m". The left cylinder has its mass around the perimeter and the right cylinder's mass is spread...
  44. Y

    Degree of Freedom for Rigid Body & Rotating CD

    Hello, how do i calculate the degree of freedom for a rigid body with 3 mass points? My guess will be 6 degrees of freedom, 3 for each mass point which gives 9, minus the 3 constraints giving 6 in total. Is this correct? what about a rotating CD in a CD player? how many degrees of freedom...
  45. E

    Understanding Degrees of Freedom in Calculating Molecule Kinetic Energy

    i need to know how many degrees do i need to be able to find the kinetic energy of the molecule ?? and may i have a brief defintion of the degree of defintion i really need to know if I really understood the meaning of the degree of definition in class and thank you
  46. B

    Understanding Particle Degree of Freedom: 3N dof for N Particles Explained

    A particle has 3 degree of freedom (dof) , so we write 3N dof for N particles... But I have a fundamental doubt: 3 dof means we consider only transitional motion of particle? ... why can't we say 6 dof?
  47. O

    Degree of freedom of two point mass

    If I have two point mass moving on a track, we say that this system has 2 degrees of freedom, because we need two independent variable to locate the point mass. But what’s the number of DOF if their (the two point mass) distance was determined? Is it one? If so, which variable can locate the two...
  48. D

    How do constraints affect the degree of freedom in particle motion?

    NOTE: This is not a homework problem. So don't move it. I was reading about degree of freedom and came to know that in general for N particles there are 3N degree of freedom that reduces when we put some constraints on their motion. E.g. For 2 particles confined in XY plane they have only 2...
  49. R

    Degree of freedom definition help

    I have been trying to learn degree of freedom and constraints by myself. However the content of these materials are very limited especially of Degree of freedom. I tried to check about these materials on the wikipedia too, but disappointed with the content about it. Can anyone provide me the...
  50. A

    Can I Use Lagrangian Equations to Calculate a Car's Response on an Uneven Road?

    So I am trying to calculate the system responsee if a car is driving 30mph over an uneven road with a bumpb of height 0.05 and a length of 20m between each bump. I have the stiffness matrix, mass matrix etc. However I am unclear about the next step, I think possibly by using the Lagrangien...