Page 113 - Robot Builders Source Book - Gordon McComb

102 Dynamic Analysis of Drives

Hence,

From the initial conditions, for t = 0,0 = 0, and 0 = a> 0, it follows that

Thus,

Differentiating Equation (3.158) we obtain for ct)(t):

For torque proportional to speed,

After transformation, this equation can be rewritten as

or

where a> is a composite solution of two components: (0 = 0)^ + 0)^
The homogeneous solution CO Q may be found in an exponential form. Thus,

Substituting the exponential form into the homogeneous variant of Equation (3.160),
we find for b

The partial solution ^ is sought in the form

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