By Leping Yang, Qingbin Zhang, Ming Zhen, Haitao Liu
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Extra resources for Dynamics and Design of Space Nets for Orbital Capture
5 Numerical Solution of Stress Waves with Characteristic Line Stress wave propagation can be solved using a hyperbolic partial differential equation. However, because of the complexity of the partial differential equation, most practical problems cannot be solved analytically, but a theoretical analysis can be used with the speciﬁed constitutive relation and boundary condition. During the process of an umbrella hatch dragging a parachute pack, the motion of the hatch provides a boundary for the connection cable and stress wave of the pack.
I et cos u ¼ BEt ¼ j en À sin u sin u cos u ! et en ! ð2:25Þ Then, the dynamic model of the cable only needs the ﬁrst two items of Eq. 24). 2 Continuous Model of Cable 25 dynamic model of the cable can be simpliﬁed into a one-dimensional model. If the cable is parallel to the OE XE axis, then, s 0 ¼ x0 ; s¼x ð2:26Þ Submitting Eq. 27) is the governing equation of the stress wave propagating in a one-dimensional elastic cable. For u ¼ ux in a one-dimensional situation, Eq. 27) can also expressed as follows, @2u E @2u @2u ¼ ¼ c2 2 2 2 @t q @x @x ð2:28Þ where c is the elastic velocity.
2 Modeling Methodology Based on the application of on-orbit capture technology, the dynamic process of space net capture is extensively being investigated from the viewpoint of project design, and the simulation system modeling issues are being analyzed conceptually and methodologically. However, the process is very complex, considering nonlinear dynamics, variable mass dynamics, and multi-body dynamics. 2 Modeling Methodology 53 600 500 F (N) 400 300 200 100 0 0 5 10 15 Δ 20 25 L (mm) Fig. 6 Tension test chart for Japan knot 800 F (N) 600 400 200 0 0 5 10 15 Δ 20 25 L (mm) Fig.
Dynamics and Design of Space Nets for Orbital Capture by Leping Yang, Qingbin Zhang, Ming Zhen, Haitao Liu