Dynamics of Partial Space Elevator with Parallel Tethers and Multiple Climbers

Li, Gangqiang; Zhu, Zheng

doi:10.1007/978-981-15-1773-0_18

Cited by 2 publications

(8 citation statements)

References 25 publications

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“…It should be pointed out that the matrix A in Eq. ( 23) is a singular matrix due to the rank-deficient submatrix M t [28]. Thus, the matrix A is not invertible in a traditional way [20], and the implicit s-stage Runge-Kutta integrator is used, that is,…”

Section: Time Integration Methodsmentioning

confidence: 99%

“…where M e is the mass matrix of element, F e and F g are the force vectors of the elastic and gravitational forces, respectively, F p;t is the force vector caused by the mass transportation across the element boundaries due to tether deployment, which vanishes when the material coordinate of the tether is fixed [21,28,29,31]. L p;k ¼ p kþ1 À p k is the element length due to variation of material coordinate.…”

Section: Finite Element Discretization Of Flexible Tethersmentioning

confidence: 99%

“…where M t is the mass matrix of tethers with detailed form in Ref. [25], X t is the position vector of tethers, F e , F g , and F p are the force vectors acting on tethers [21,28]. The lumped masses of the remote units are added into the mass matrix M t of the tethers in the corresponding places for the connecting nodes [25].…”

Section: Finite Element Discretization Of Flexible Tethersmentioning

confidence: 99%

“…The second approach is superior to the first approach for the current study due to the easy implementation of kinematic constraints of the connection relationship between the central spacecraft and multiple tethers. Recently, the authors proposed a nodal position finite element method in the ALE description (NPFE-M_ALE) to study the variable-length tether problem in the space elevator with moving climbers [21,28,29]. Furthermore, the finite element model of variablelength tether embedded with the second approach is also used for the space tether systems [24,27].…”

Section: Introductionmentioning

confidence: 99%

“…This leads to the violation of constraint equations in the differential equations and generates unreliable results [27]. To address these mentioned limitations, the NPFEM_ALE model of the space elevator [21,25,28,29] is extended and applied to the tether deployment problem of E-sail. Furthermore, a framework of an implicit Runge-Kutta implicit time integration with s stages and a symplectic property for solving the differential-algebraic equations is developed.…”

Section: Introductionmentioning

confidence: 99%

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Stability and control of radial deployment of electric solar wind sail

Zhu

2021

Nonlinear Dyn

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The paper studies the stability and control of radial deployment of an electric solar wind sail with the consideration of high-order modes of elastic tethers. The electric solar wind sail is modeled by combining the flexible tether dynamics, the rigid-body dynamics of central spacecraft, and the flexible-rigid kinematic coupling. The tether deployment process is modeled by the nodal position finite element method in the arbitrary Lagrangian-Eulerian framework. A symplectic-type implicit Runge-Kutta integration is proposed to solve the resulting differential-algebraic equation. A proportional-derivative control strategy is applied to stabilize the central spacecraft's attitudes to ensure tethers' stable deployment with a constant spinning rate. The results show the electric solar wind sail requires thrust at remote units in the tangential direction to counterbalance the Coriolis forces acting on the tethers and remote units to deploy tethers radially successfully. The parametric analysis shows the tether deployment speed and the thrust magnitude significantly impacts deployment stability and tether libration, which opens the possibility of successful deployment of tethers by using optimal control. Finally, the analysis results show that radial deployment is advantageous due to the isolated deployment mechanism, and a jammed tether can be isolated from affecting the deployment of rest tethers.Keywords Space tether Á Electric solar wind sail Á Multibody dynamics Á Rigid-flexible coupling Á Flexible structural stability Á Nodal position finite element method Á Arbitrary Lagrangian-Eulerian

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Section: Time Integration Methodsmentioning

confidence: 99%

Section: Finite Element Discretization Of Flexible Tethersmentioning

confidence: 99%

Section: Finite Element Discretization Of Flexible Tethersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability and control of radial deployment of electric solar wind sail

Zhu

2021

Nonlinear Dyn

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The Orbital Mechanics of Space Elevator Launch Systems

Peet

2020

Preprint

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The construction of a space elevator would be an inspiring feat of planetary engineering of immense cost and risk. But would the benefit outweigh the costs and risks? What, precisely, is the purpose for building such a structure? For example, what if the space elevator could provide propellant-free (free release) orbital transfer to every planet in the solar system and beyond on a daily basis? In our view, this benefit might outweigh the costs and risks. But can a space elevator provide such a service? In this manuscript, we examine 3 tiers of space elevator launch system design and provide a detailed mathematical analysis of the orbital mechanics of spacecraft utilizing such designs. We find the limiting factor in all designs is the problem of transition to the ecliptic plane. For Tiers 1 and 2, we find that free release transfers to all the outer planets is possible, achieving velocities far beyond the ability of current Earth-based rocket technology, but with significant gaps in coverage due to planetary alignment. For Tier 3 elevators, however, we find that fast free release transfers to all planets in the solar system are possible on a daily basis. Finally, we show that Tier 2 and 3 space elevators can potentially use counterweights to perform staged slingshot maneuvers, providing a velocity multiplier which could dramatically reduce transit times to outer planets and interstellar destinations.

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Dynamics of Partial Space Elevator with Parallel Tethers and Multiple Climbers

Cited by 2 publications

References 25 publications

Stability and control of radial deployment of electric solar wind sail

Stability and control of radial deployment of electric solar wind sail

The Orbital Mechanics of Space Elevator Launch Systems

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