一由載物衛星,鋼索,探測衛星所成系統之動力研究

Abstract

考慮一個只受重力作用,由鋼索將探測衛星聯結於載物衛星上的系統.對這 系統,本文建立了它的運動模式.假設鋼索具有不可伸展的特性,本文運用 分離變數法來探討此狀態下系統之解的存在性問題.對此狀態下的系統,本 文也導出它的兩種平衡解:一為似放射狀的平衡解,一為似圓弧狀的平衡 解.取消對鋼索不可伸展性的假設後,本文求得系統也存在一似放射狀的平 衡解.本文更進一步的將系統的總能量當成一Liapunov函數,來研究系統在 此平衡解上的穩定條件. The model equations describing the motions of a carrier satellite and a probe satellite connected by a long cable in centrifugal gravitational field was constructed. Time dependent solutions of the system with cable made of inextensible material was discussed, using the method of separation of variables. Some stationary solutions of radial type and circular type are derived. The total energy of the system was used as a Liapunov function to study the stability of the radial stationary solutions without assuming the inextensibility of the cable.