The phrase "degrees of freedom" is used in three different branches of science: in physics and physical chemistry, in mechanical engineering and aerospace engineering engineering, and in statistics. The three usages are linked historically and through the underlying mathematics through the concept of dimensionality, but they are not identical. ==Physics and chemistry== In physics and chemistry, each independent mode in which a particle or system may move or be oriented is one degree of freedom. For a roughly dumbbell-shaped hydrogen molecule, three such modes would be rotation (twirling), translation (hurtling through space) and vibration (the two dumbbell "balls" bouncing together and apart). According to the equipartition theorem of thermodynamics, in case of thermal equilibrium each degree of freedom in every particle of a system will contain the same energy on average (equal to ''kT'', the thermodynamic temperature of the system multiplied by the fundamental Boltzmann constant). However, thermal equilibrium can only be reached among interacting particles, a process called thermalisation. According to quantum mechanics and more specifically Werner Heisenberg uncertainty principle, the amount of energy within any degree of freedom is never zero, but is always at least equal to the zero-point energy for that mode. ==Engineering== In mechanical engineering, Aerospace engineering and robotics, degrees of freedom (DOF) describes flexibility of motion. A mechanism or Linkage (mechanical) that has complete freedom of motion (even if only in a limited area, or envelope) has six degrees of freedom. Three modes are translation - the ability to move in each of three dimensions. Three are rotation, or the ability to change angle around three perpendicular axes. To put it in simpler terms, each of the following is one degree of freedom: #Moving up and down (heave); #moving left and right (sway); #moving forward and back (surge); #tilting up and down (flight dynamicsing); #turning left and right (flight dynamicsing); #tilting side to side (flight dynamicsing). See also: Euler angles. In robotics, ''degrees of freedom'' is often used to describe the number of directions that a robot can pivot or move a joint. A human arm is considered to have 7 DOF. A shoulder gives pitch, yaw and roll, an elbow allows for pitch, and a wrist allows for pitch, yaw and roll. Only 3 of those movements would be necessary to move the hand to any point in space, but people would lack the ability to grasp things from different angles or directions. ==Statistics== In statistics, degrees of freedom are the number of values in probability distributions that are free to be varied. Examples of this statistical parameter include the chi-square distribution, the F-distribution, Student's t-distribution, and the beta distribution that underlies them. See Pearson's chi-square test and analysis of variance for more information. In the familiar uses of these distributions, the degrees of freedom takes only integer values (usually low ones). The underlying mathematics do allow for fractional degrees of freedom, which can arise in more sophisticated uses. Technical terminology su:Tingkat kabebasan
In the ancient past, I failed a statistics class in which the professor blathered on about degrees of freedom as though I cared, but this page doesn't mention it. If I was supposed to have learned is one of the two meanings used in the article, the word ''statistics'' should probably be mentioned (with a link), otherwise the statistical meaning is necessary. User:TUF-KAT :Thanks User:TUF-KAT I'm not going to mess with that half of it. :-) User:EasilyAmused My Stats teacher right now is having a terrible time explaining degrees of freedom, and I can't figure it out... this page is no help. Hopefully when I figure it out I can provide a better explanation. -User:booyabazooka
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Words begining with Degrees_of_freedom:
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Degrees of freedom
The phrase "degrees of freedom" is used in three different branches of science: in physics and physical chemistry, in mechanical engineering and aerospace engineering engineering, and in statistics. The three usages are linked historically and through the underlying mathematics through the concept of dimensionality, but they are not identical. ==Physics and chemistry== In physics and chemistry, each independent mode in which a particle or system may move or be oriented is one degree of freedom. For a roughly dumbbell-shaped hydrogen molecule, three such modes would be rotation (twirling), translation (hurtling through space) and vibration (the two dumbbell "balls" bouncing together and apart). According to the equipartition theorem of thermodynamics, in case of thermal equilibrium each degree of freedom in every particle of a system will contain the same energy on average (equal to ''kT'', the thermodynamic temperature of the system multiplied by the fundamental Boltzmann constant). However, thermal equilibrium can only be reached among interacting particles, a process called thermalisation. According to quantum mechanics and more specifically Werner Heisenberg uncertainty principle, the amount of energy within any degree of freedom is never zero, but is always at least equal to the zero-point energy for that mode. ==Engineering== In mechanical engineering, Aerospace engineering and robotics, degrees of freedom (DOF) describes flexibility of motion. A mechanism or Linkage (mechanical) that has complete freedom of motion (even if only in a limited area, or envelope) has six degrees of freedom. Three modes are translation - the ability to move in each of three dimensions. Three are rotation, or the ability to change angle around three perpendicular axes. To put it in simpler terms, each of the following is one degree of freedom: #Moving up and down (heave); #moving left and right (sway); #moving forward and back (surge); #tilting up and down (flight dynamicsing); #turning left and right (flight dynamicsing); #tilting side to side (flight dynamicsing). See also: Euler angles. In robotics, ''degrees of freedom'' is often used to describe the number of directions that a robot can pivot or move a joint. A human arm is considered to have 7 DOF. A shoulder gives pitch, yaw and roll, an elbow allows for pitch, and a wrist allows for pitch, yaw and roll. Only 3 of those movements would be necessary to move the hand to any point in space, but people would lack the ability to grasp things from different angles or directions. ==Statistics== In statistics, degrees of freedom are the number of values in probability distributions that are free to be varied. Examples of this statistical parameter include the chi-square distribution, the F-distribution, Student's t-distribution, and the beta distribution that underlies them. See Pearson's chi-square test and analysis of variance for more information. In the familiar uses of these distributions, the degrees of freedom takes only integer values (usually low ones). The underlying mathematics do allow for fractional degrees of freedom, which can arise in more sophisticated uses. Technical terminology su:Tingkat kabebasan
Degrees of freedom
In the ancient past, I failed a statistics class in which the professor blathered on about degrees of freedom as though I cared, but this page doesn't mention it. If I was supposed to have learned is one of the two meanings used in the article, the word ''statistics'' should probably be mentioned (with a link), otherwise the statistical meaning is necessary. User:TUF-KAT :Thanks User:TUF-KAT I'm not going to mess with that half of it. :-) User:EasilyAmused My Stats teacher right now is having a terrible time explaining degrees of freedom, and I can't figure it out... this page is no help. Hopefully when I figure it out I can provide a better explanation. -User:booyabazooka
See other meanings of words starting from letter:
D
DA | DB | DC | DE | DF | DG | DH | DI | DJ | DK | DL | DM | DN | DO | DP | DR | DS | DT | DU | DW | DX | DY | DZ |Words begining with Degrees_of_freedom:
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Degrees_of_freedom
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