Just use Newton's law of universal gravitation with your initial conditions to find the instantaneous acceleration involved.
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In Newton Euler equations, " translational acceleration " is used to mean the instantaneous acceleration of the centre of mass of a body.
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Due to only tracking the peak instantaneous acceleration the SRS does not contain all the information in the transient waveform from which it was created.
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The instantaneous acceleration is the limit of the ratio \ Delta \ mathbf { v } and \ Delta t as \ Delta t approaches zero i . e .,
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You could solve the equation for the curve shape of the rope assuming it was completely flexible and its instantaneous acceleration around the curve was given by the tension and curvature.
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:: : : : : You're quite right, but the point of this isn't really for accuracy with regard to instantaneous acceleration, average will do just fine.
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As seen by the three green tangent lines in the figure, an object's instantaneous acceleration at a point in time is the slope of the line tangent to the curve of a ( vs . graph at that point.
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A human-crewed Orion, however, must use some sort of damping system behind the pusher plate to smooth the instantaneous acceleration to a level that humans can comfortably withstand typically about 2 to 4 " g ".
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This means that, if force is constant, instantaneous acceleration of an object is inversely proportional to the mass of that object, i . e . the " rate of change " of velocity " decreases " the greater the mass of a body.
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If a velocity loop PID controller is being used to control the speed of the load and command the force being applied by the actuator, then it is beneficial to take the desired instantaneous acceleration, scale that value appropriately and add it to the output of the PID velocity loop controller.
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