Degrees of freedom sentence example

degrees of freedom
  • Instead of following the motion of each individual part of a material system, he showed that, if we determine its configuration by a sufficient number of variables, whose number is that of the degrees of freedom to move (there being as many equations as the system has degrees of freedom), the kinetic and potential energies of the system can be expressed in terms of these, and the differential equations of motion thence deduced by simple differentiation.
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  • If the molecules and molecular aggregates were more complicated, and the number of degrees of freedom of the aggregates were limited to 6, or were the same as for single molecules, we should have n-= so/R.
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  • The present writer drew attention to this difficulty as far back as 1881, 1 when he pointed out that the different intensities of different spectral lines need not involve the consequence that in an enclosure of uniform temperature the energy is unequally partitioned between the corresponding degrees of freedom.
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  • The number F is called the number of degrees of freedom of the system, and is measured by the excess of the number of unknowns over the number of variables.
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  • In 1879 Maxwell Considered It One Of The Greatest Difficulties Which The Kinetic Theory Had Yet Encountered, That In Spite Of The Many Other Degrees Of Freedom Of Vibration Revealed By The Spectroscope, The Experimental Value Of The Ratio S/S Was 1.40 For So Many Gases, Instead Of Being Less Than 4/3.
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  • A Hypothesis Doubtfully Attributed To Maxwell Is That Each Additional Atom In The Molecule Is Equivalent To Two Extra Degrees Of Freedom.
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  • 1900) adopted the mean value n=3.5, and also assumed the specific heat at constant volume s =3.5 R (which gives So=4.5 R) on the basis of an hypothesis, doubtfully attributed to Maxwell, that the number of degrees of freedom of a molecule with m atoms is 2m +I.
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  • The lamina when perfectly free to move in its own plane is said to have three degrees of freedom.
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  • Hence a rigid body not constrained in any way is said to have six degrees of freedom.
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  • The quantities E, v I, ?~, u, are no longer: independent, and the body has now only five degrees of freedom.
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  • Every additional constraint introduces an additional equation of the type (10) and reduces the number of degrees of freedom by one.
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  • Balls Theory of Screws an analysis is made of the possible displacements of a b~dy which has respectively two, three, four, five degrees of freedom.
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  • It follows that when a body has two degrees Of freedom it can twist about any one of a singly infinite system of screws whose axes lie on a certain cylindroid.
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  • These co-ordinates may be chosen in an endless variety of ways, but their number is determinate, and expresses the number of degrees of freedom of the system.
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  • \M vibration of this character is called a normal mode ~ of vibration of the system; the number n of such modes is equal to that of the degrees of freedom ~ \ possessed by the system.
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  • The case of three degrees of freedom is instructive on account of the geometrical analogies.
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  • When there are n degrees of freedom we have from (3)
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  • The most important applications of the theory of vibrations are to the case of continuous systems such as strings, bars, membranes, plates, columns of air, where the number of degrees of freedom is infinite.
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  • In a five-bar chain a point, as a, in a link non-adjacent to the fixed link has two degrees of freedom and the chain cannot therefore be used for a mechanism.
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  • denominator degrees of freedom (because F is actually a ratio ).
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  • haptic interfaces typically take the form of a framework with multiple degrees of freedom.
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  • numerator degrees of freedom are given first.
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  • self-excited vibrations of mechanical systems using parametric excitation in two degrees of freedom.
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  • The peculiar status of rigid bodies is that the principles in question are in most cases sufficient for the complete determination of the motion, the dynamical equations (I or 2) being equal in number to the degrees of freedom (six) of a rigid solid, whereas in cases where the freedom is greater we have to invoke the aid of other supplementary physical hypotheses (cf.
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  • We discuss the possibility of suppressing self-excited vibrations of mechanical systems using parametric excitation in two degrees of freedom.
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