Analysis of Spinning Spacecraft with Wire Booms, Part 2: Out of Plane Dynamics and Maneuvers

Free-Space Dynamics and Control of the Rotary-Motion Extended Array Synthesis Spacecraft Concept

“…This indicates that the in-plane and out-of-plane motions can be separated. This matches earlier work [10,11] that found that in-plane and out-ofplane motions were separable. Ignoring the dependence on the rates, the equations for l, θ and ϕ can be written as x ::::…”

“…It is modeled here, as in Ref. [10], by a viscous force. When the tethers are stretched (l 1 ; l 2 > l 0 ), the tether forces acting on the end masses are then given by…”

“…The tether spring and damping coefficients are taken from Refs. [10,16]. The tethers will stretch to compensate for the centripetal acceleration of the end antenna arrays, and their equilibrium length is l eq mω 2 0 R kl 0 ∕k − mω 2 0 ≈ 40.53 m. The initial state is listed in Table 2.…”

“…Both the Van Allen Probes [9][10][11] and MMS [13,17] missions were controlled based on the hub state rather than the hub and the tethers. This has the major benefit of not needing to sense the angles θ and ϕ for each tether.…”

“…More recently, the Van Allen probes (also known as radiation belt storm probes) mission launched in 2012 with four 20 m booms spinning near 3 rpm with end masses of ∼200 g. Their dynamics are discussed both in and out of plane in Refs. [9][10][11]. Even more recently, the Magnetospheric Multiscale (MMS) mission launched in 2015 with four 60 m booms also held in tension by the 3 rpm spin.…”