Degrees of freedom Sentence Examples
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.
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.
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.
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.
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.Advertisement
The lamina when perfectly free to move in its own plane is said to have three degrees of freedom.
Hence a rigid body not constrained in any way is said to have six degrees of freedom.
Every additional constraint introduces an additional equation of the type (10) and reduces the number of degrees of freedom by one.
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.
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.Advertisement
The case of three degrees of freedom is instructive on account of the geometrical analogies.
When there are n degrees of freedom we have from (3)
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.
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.
We discuss the possibility of suppressing self-excited vibrations of mechanical systems using parametric excitation in two degrees of freedom.Advertisement