Necessary and Sufficient Conditions of Rolling and Sliding of a Spherical Shell in a Helical Channel

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We investigate the conditions when the motion of a heavy ball in a helical channel takes the form of rolling or rolling with partial sliding. This problem is relevant for the manufacturing technology of unsuspended spherical laser targets being developed at the thermonuclear target laboratory at the Lebedev Physics Institute of the Russian Academy of Sciences. While moving through the cryostat channel, the laser target may slide part of the way, which causes undesirable damage to its surface. We study the possible motion regimes with the objective of determining the optimal regime that minimizes the sliding length.