By Leping Yang, Qingbin Zhang, Ming Zhen, Haitao Liu
This ebook covers the themes of theoretical ideas, dynamics version and set of rules, venture research, method layout and experimental stories of area nets procedure, aiming to supply an preliminary framework during this box and function a prepared reference for these . area nets approach represents a vanguard box in destiny improvement of aerospace applied sciences. although, it consists of new demanding situations and difficulties similar to nonlinear and distorted nets constitution, advanced inflexible versatile coupling dynamics, orbital move of house versatile composite and dynamics keep an eye on. at the moment, no complete books on area nets dynamics and layout can be found, so power readers can get to grasp the operating mechanism, dynamics components, and challenge layout of the gap nets method from a chinese language perspective.
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Extra resources for Dynamics and Design of Space Nets for Orbital Capture
1 Knotting method Flat knot Japan knot No knot Fracture strength/N 488 512 627 Basic Assumption Because the net and connecting tether are both full flexible bodies, the tether-net dynamics is governed by complicated nonlinear equations. Therefore, establishing the dynamics of the system in detail is complex. We started the study using the following simpliﬁed assumptions: 54 3 Dynamics of Space Nets (1) The tether cannot bear compression, and longitudinal elasticity and damping are taken into account.
91), the recurrence relation of the cable element acceleration (an:x , an:y , an:z ) is as follows, 3 2 3 3 2 an:x anÀ1:x À½ðu_ n Þ2 þ ðh_ n Þ2 cos hn cos un þ 2h_ n u_ n sin hn sin un 7 6 7 7 6 6 5 4 an:y 5 ¼ 4 anÀ1:y 5 þ Ln 4 Àðh_ n Þ2 sin hn 2 2 _ _ an:z anÀ1:z À½ðu_ n Þ þ ðhn Þ cos hn sin un À 2hn u_ n sin hn cos un 3 2 € € n cos hn sin un Àhn sin hn cos un À u 7 6 þ Ln 4 5 N ¼ 1; 2; . 91) are obviously the geometric constraint and motion constraint of the cable system, respectively. ), and the forces loaded on the nth cable end are marked as Fn ðFn:x ; Fn:y ; Fn:z Þ.
The position of point P at the cable in the cable coordinates is denoted as s, and r is deﬁned as the position vector in the inertial space. We then obtain r ¼ xi þ yj þ zk ð2:8Þ s Fig. 3 Coordinate system of space cable n s0 P0 b ZE r 0 u P t r OE XE YE 22 2 Cable Dynamics Elements where i, j, and k are unit vectors in three directions in the inertial space, and ðx; y; zÞ are the coordinates of point P in the inertial space. Based on the spatial arc length formula, the following relationship exists between position s of point P in the cable coordinates and space coordinates: Zp s¼ 0 ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ s 2 2 @x 2 @y @z þ þ ds @s @s @s ð2:9Þ The local Frenet coordinate system Ptnb is developed with P as the base point, where axes Pt, Pn, and Pb are directed in the local tangent direction, main normal direction, and binormal direction, respectively, and et , en , and eb are the corresponding unit vectors, according to the differential geometry theory, et ¼ @r @s ð2:10Þ From the Frenet equation of the space curve, the unit vectors in three directions satisfy the following relationship: 2 3 2 e 0 d4 t5 4 en ¼ Àj ds 0 eb j 0 Às 32 3 0 et s 5 4 en 5 0 eb ð2:11Þ where j and s are respectively the curvature and torsion of point P.
Dynamics and Design of Space Nets for Orbital Capture by Leping Yang, Qingbin Zhang, Ming Zhen, Haitao Liu