In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the...In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.展开更多
Let Xi,X2,... ,Xk be k disjoint subsets of S with the same cardinality m. Define H（m,k） = {X lahtain in S ： X ￠Xi for 1 ≤ i≤ k} and P（m,k） = {X lohtain ni S ： X ∩ Xi ≠0 for at least two Xi＇s}. Suppose S=U...Let Xi,X2,... ,Xk be k disjoint subsets of S with the same cardinality m. Define H（m,k） = {X lahtain in S ： X ￠Xi for 1 ≤ i≤ k} and P（m,k） = {X lohtain ni S ： X ∩ Xi ≠0 for at least two Xi＇s}. Suppose S=Ui=1^k Xi , and let Q（m, k, 2） be the collection of all subsets K of S satisfying ｜K ∩ Xi｜ ≥ 2 for some 1 ≤ i ≤ k. For any two disjoint subsets Yi and Y2 of S, we define F1,j = {X lahtain in S ： either ｜X ∩Y1｜≥1 or ｜X ∩ Y2｜≥ j}. It is obvious that the four posets are graded posets ordered by inclusion. In this paper we will prove that the four posets are nested chain orders.展开更多
基金Project (51475411) supported by the National Natural Science Foundation of ChinaProject (LY15E070002) supported by Zhejiang Provincial Natural Science Foundation of China
文摘In order to control the growth of space debris,a novel tethered space robot(TSR) was put forward.After capture,the platform,tether,and target constituted a tethered combination system.General nonlinear dynamics of the tethered combination system in the post-capture phase was established with the consideration of the attitudes of two spacecrafts and the quadratic nonlinear elasticity of the tether.The motion law of the tethered combination in the deorbiting process with different disturbances was simulated and discussed on the premise that the platform was only controlled by a constant thrust force.It is known that the four motion freedoms of the tethered combination are coupled with each other in the deorbiting process from the simulation results.A noticeable phenomenon is that the tether longitudinal vibration does not decay to vanish even under the large tether damping with initial attitude disturbances due to the coupling effect.The approximate analytical solutions of the dynamics for a simplified model are obtained through the perturbation method.The condition of the inter resonance phenomenon is the frequency ratio λ_1=2.The case study shows good accordance between the analytical solutions and numerical results,indicating the effectiveness and correctness of approximate analytical solutions.
基金the National Natural Science Foundation of China （No. 10471016）.
文摘Let Xi,X2,... ,Xk be k disjoint subsets of S with the same cardinality m. Define H（m,k） = {X lahtain in S ： X ￠Xi for 1 ≤ i≤ k} and P（m,k） = {X lohtain ni S ： X ∩ Xi ≠0 for at least two Xi＇s}. Suppose S=Ui=1^k Xi , and let Q（m, k, 2） be the collection of all subsets K of S satisfying ｜K ∩ Xi｜ ≥ 2 for some 1 ≤ i ≤ k. For any two disjoint subsets Yi and Y2 of S, we define F1,j = {X lahtain in S ： either ｜X ∩Y1｜≥1 or ｜X ∩ Y2｜≥ j}. It is obvious that the four posets are graded posets ordered by inclusion. In this paper we will prove that the four posets are nested chain orders.
