# Download Mathematical Machines: Analog Devices, Volume 2 by Francis J. Murray PDF

By Francis J. Murray

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Extra resources for Mathematical Machines: Analog Devices, Volume 2

Sample text

And y, but it may very well give a poor relation between x and y. One would expect that y might x. To produce a match lag behind or overshoot will of jc and y one should not try to match x and y directly. The above a simple case which represents Most problems, occurs in computing devices. however, involving servomechanisms require a more complicated response than the one de To obtain sucharesponse a theory of servomechanisms has been set up analogous scribed above. to electrical circuits (see, for example, H.

Sometimes it is useful course, is to have variations of this in which the slot which guides the pin is moveable or if fixed is not radial Logarithmic multiplication does not permit a change of sign. An alternate method of multiply ing is that of "quarter squares" based on the Fig, formula to "(^ permit more than one turn of the main disk, provision must be Notice that Eq. 1 involves addition, subtraction, parallel to itself. made to move This motion is We will return to this point.

Consequently, equations may be written y = a^x + a^y + z = now Let us vector u 3jl + x it is = Au. 6 satisfying Eq. 6) condition that a I will exist that the is determinant of the coefficients be zero. , + 99 these. w = (y + the must + 0n + lengths latter involves an does not correspond to any possible motion of a rigid body. then assume: If a motion of a rigid body leaves one point on a line unchanged. , each is Newton s it is laws, necessary to consider w= placed relative to an axis, . is particularly is an axis of it is clear that a torque must be applied around the axis to effect the rate of rotation around this axis.