Circular Mass Accelerator

This Demonstration is a simulation of a circular mass accelerator based on the principle of the hula hoop [1].
A mass sliding with very little friction inside a tubular ring can be accelerated to very high speeds. The accelerator ring gyrates eccentrically with a very low amplitude at an ever-increasing angular speed while keeping the mass in phase with its own rotation. When the desired speed is finally reached, the mass is released from the ring and hurled into the atmosphere.
There are projects [3] that use this principle to launch material supplies into orbit much more economically than by using more conventional rocket spacecrafts.

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DETAILS

A sled slides with a friction coefficient at angular position inside a ring of radius gyrating with eccentricity .
Gravity is neglected, as it is relatively small. From the equilibrium of centripetal and frictional forces acting on the sled and the geometry of the mechanism, the equation of motion [1, 2] is .
The values for , , and being very small, the equation can be simplified to .
This ODE can now be solved symbolically to give .
This Demonstration only gives a qualitative simulation of a mass accelerator. To see details about a real project (the Slingatron) see [3] and [4].
References
[1] A. O. Belyakov and A. P. Seyranian. "Regular Dynamics of a Hula-Hoop." istina.msu.ru/media/publications/articles/1bf/e6e/458523/Belyakov_A_O.pdf.
[2] D. A. Tidman, Slingatron—A Mechanical Hypervelocity Mass Accelerator, Sandy, UT: Aardvark Global Publishing, 2007. www.amazon.com/Slingatron-Mechanical-Hypervelocity-Mass-Accelerator/dp/1427626588.
[3] D. A. Tidman and F. D. Witherspoon, "Slingatron—A Mechanical Hypervelocity Sling," presentation given at Capital Science Conference (CSC 2008), Washington, DC. www.washacadsci.org/activities-and-events/capsci-abstracts/capital-science-2008/#tidman.
[4] A. Nowicki. "Slingatron with Magnetic Bearing." (Sept 23, 2006) www.islandone.org/LEOBiblio/SPBI125.HTM.
http://www.washacadsci.org/capsci08/presentations/ASTI-tidman.pdf
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