Hence M. = Jo. + K . - (1/2)MR2 sin(2. ) ((2 is the torque required to be produced by the muscles to maintain the haltere in simple harmonic motion.
Here the interest is in the (instantaneous) torque around the pivot in the XY plane, M(, due to the input pitch angular velocity,. . One can write,
■lil = Mr2( = MR2 sin2(: )( = MR2(1/2)[1 - cos(2: )] 2.7-8
d . = MR2$(1/2) - MR>(l/2) cos(2. ) + MR2$. sin(2. ) 2.7-9
M^ = $(1/2)MR2 - $(1/2)MR2 cos(2. ) + (l/2)MR2$. sin(2. ) 2.7-10
Because |2. m| > 10° in the haltere system, one cannot use the approximations: sin(2.) . 2., and sin2(.) . .2. The M$ moment can be written:
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