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Waverider has high lift to drag ratio and will be an idea aerodynamic configuration for hypersonic vehicles. But a structure permitting aerodynamic like waverider is still difficult to generate under airframe’s geometric constrains using traditional waverider design methods. And furthermore, traditional waverider’s aerodynamic compression ability cannot be easily adjusted to satisfy the inlet entrance requirements for hypersonic air-breathing vehicles. The purpose of this paper is to present a new method named osculating general curved cone (OCC) method aimed to improve the shortcomings of traditional waveriders.

A basic curved cone is, first, designed by the method of characteristics. Then the waverider’s inlet captured curve and front captured tube are defined in the waverider’s exit plane. Osculating planes are generated along the inlet captured curve and the designed curved cone is transformed to the osculating planes. Streamlines are traced in the transformed curved cone flow field. Combining all streamlines which have been obtained, OCC waverider’s compression surface is generated. Waverider’s upper surface uses the free stream surface.

It is found that OCC waverider has good volumetric characteristics and good flow compression abilities compared with the traditional osculating cone (OC) waverider. The volume of OCC waverider is 25 per cent larger than OC waverider at the same design condition. Furthermore, OCC waverider can compress incoming flow to required flow conditions with high total pressure recovery in the waverider’s exit plane. The flow uniformity in the waverider exit plane is quite well.

The analyzed results show that the OCC waverider can be a practical high performance airframe/forebody for hypersonic vehicles. Furthermore, this novel waverider design method can be used to design a structure permitting aerodynamic like waverider for a practical hypersonic vehicle.

The paper puts forward a novel waverider design method which can improve the waverider’s volumetric characteristics and compression abilities compared with the traditional waverider design methods. This novel design approach can extend the waverider’s applications for designing hypersonic vehicles.

The purpose of this study is to obtain the differential geometric analysis of autonomous wheel-legged robots and their trajectories on the terrain.

The author uses a wheel using the osculating sphere of the curve on rough terrain. Additionally, the author expresses a triple osculating sphere wheel by taking advantage of differential geometry. Moreover, the author examined the consecutive wheel center-curves to obtain the optimum posture of a micro-hydraulic toolkit (MHT) robot.

The author examined the terrain path, which is crucial for trajectory planning in terms of the geometric perspective. The author designed the triple MHT wheel using the osculating sphere of the MHT robot trajectory by taking advantage of local differential geometric properties of this curve on the terrain. The consecutive wheel center-curves were expressed and studied based on differential geometry.

The author provides a novel approach for the optimum posture of an MHT robot using consecutive wheel-center curves and provides an original perspective to MHT robot and its trajectory by using differential geometry.

This paper aims to provide a series of new methods for projecting a three-dimensional (3D) object onto a free-form surface. The projection algorithms presented can be divided into three types, namely, orthogonal, perspective and parallel projection.

For parametric surfaces, the computing strategy of the algorithm is to obtain an approximate solution by using a geometric algorithm, then improve the accuracy of the approximate solution using the Newton–Raphson iteration. For perspective projection and parallel projection on an implicit surface, the strategy replaces Newton–Raphson iteration by multi-segment tracing. The implementation takes two mesh objects as an example of calculating an image projected onto parametric and implicit surfaces. Moreover, a comparison is made for orthogonal projections with Hu’s and Liu’s methods.

The results show that the new method can solve the 3D objects projection problem in an effective manner. For orthogonal projection, the time taken by the new method is substantially less than that required for Hu’s method. The new method is also more accurate and faster than Liu’s approach, particularly when the 3D object has a large number of points.

The algorithms presented in this paper can be applied in many industrial applications such as computer aided design, computer graphics and computer vision.

This paper aims to provide a new method to design a fuel efficient control strategy such as J₂ perturbation for deploying a constellation into a specified configuration. The nonspherical perturbation, mainly J₂ perturbation, is the dominant perturbation for low-Earth-orbit (LEO) satellites of a constellation. This perturbation can be utilized in the control strategy to lower fuel consumption enormously.

The relationship of the coupled variables, the relative right ascension of ascending node (RAAN) and the relative phase (RP), are analyzed. First-order approximation expressions of the relative RAAN (RRAAN) and the relative phase (RP) with respect to the semimajor axis are derived. According to the Gauss’ variational equations, the reduced explicit functions of these variables in regard to each active control are established. Based on these functions, control strategy design methods, including the preliminary planning and iterative corrections, are proposed. The numerical simulation is carried out to verify the proposed method.

The results indicate that the constellation can be deployed accurately about the semimajor axis, the RRAAN and the relative phase (RP) by the developed fuel efficient control strategy.

The proposed control strategy is limited for the orbital altitude where the J₂ perturbation is dominant.

The proposed effective method is applicable for the engineers planning an orbital control strategy of deploying satellites of a constellation.

The new control strategy can realize utilization of J₂ perturbation and an accurate deployment, simultaneously. Further, this paper provides practical help for satellite engineers.

The purpose of this paper is to develop a discrete element (DE) and multiscale modeling methodology to represent granular media at their particle scale as they interface solid deformable bodies, such as soil‐tool, tire, penetrometer, pile, etc., interfaces.

A three‐dimensional ellipsoidal discrete element method (DEM) is developed to more physically represent particle shape in granular media while retaining the efficiency of smooth contact interface conditions for computation. DE coupling to finite element (FE) facets is presented to demonstrate initially the development of overlapping bridging scale methods for concurrent multiscale modeling of granular media.

A closed‐form solution of ellipsoidal particle contact resolution and stiffness is presented and demonstrated for two particle, and many particle contact simulations, during gravity deposition, and quasi‐static oedometer, triaxial compression, and pile penetration. The DE‐FE facet coupling demonstrates the potential to alleviate artificial boundary effects in the shear deformation region between DEM granular media and deformable solid bodies.

The research is being extended to couple more robustly the ellipsoidal DEM code and a higher order continuum FE code via overlapping bridging scale methods, in order to remove dependence of penetration/shear resistance on the boundary placement for DE simulation.

When concurrent multiscale computational modeling of interface conditions between deformable solid bodies and granular materials reaches maturity, modelers will be able to simulate the mechanical behavior accounting for physical particle sizes and flow in the interface region, and thus design their tool, tire, penetrometer, or pile accordingly.

A closed‐form solution for ellipsoidal particle contact is demonstrated in this paper, and the ability to couple DE to FE facets.

The purpose of this paper is to study the effect of J₃ perturbation of the Earth’s oblateness on satellite orbit compared with J₂ perturbation.

Based on the parametric variation method in the time domain, considering more accurate Earth potential function by considering J₃-perturbation effect, the perturbation equations about satellite’s six orbital elements (including semi-major axis, orbit inclination, right ascension of the ascending node, true anomaly, eccentricity and argument of perigee) has been deduced theoretically. The disturbance effects of J₂ and J₃ perturbations on the satellite orbit with different orbit inclinations have been studied numerically.

With the inclination increasing, the maximum of the semi-major axis increases weakly. The difference of inclination disturbed by the J₂ and J₃ perturbation is relative to orbit inclinations. J₃ perturbation has weak effect on the right ascension and argument of perigee. The critical angle of the right ascension and argument of perigee which decides the precession direction is 90° and 63.43°, respectively. The disturbance effects of J₂ and J₃ perturbations on the argument of perigee, right ascension and eccentricity are weakened when the eccentricity increases, simultaneously, the difference of J₂ and J₃ perturbations on argument of perigee, right ascension and argument of perigee decreases with eccentricity increasing, respectively.

In the future, satellites need to orbit the Earth much more precisely for a long period. The J₃ perturbation effect and the weight compared to J₂ perturbation in LEO can provide a theoretical reference for researchers who want to improve the control accuracy of satellite. On the other hand, the theoretical analysis and simulation results can help people to design the satellite orbit to avoid or diminish the disturbance effect of the Earth’s oblateness.

The J₃ perturbation equations of satellite orbit elements are deduced theoretically by using parametric variation method in this paper. Additionally, the comparison studies of J₂ perturbation and J₃ perturbation of the Earth’s oblateness on the satellite orbit with different initial conditions are presented.

In this paper, we consider the Heisenberg groups which play a crucial role in both geometry and theoretical physics.

In the first part, we retrieve the geometry of left-invariant Randers metrics on the Heisenberg group H_2n+1, of dimension 2n + 1. Considering a left-invariant Randers metric, we give the Levi-Civita connection, curvature tensor, Ricci tensor and scalar curvature and show the Heisenberg groups H_2n+1 have constant negative scalar curvature.

In the second part, we present our main results. We show that the Heisenberg group H_2n+1 cannot admit Randers metric of Berwald and Ricci-quadratic Douglas types. Finally, the flag curvature of Z-Randers metrics in some special directions is obtained which shows that there exist flags of strictly negative and strictly positive curvatures.

In this work, we present complete Reimannian geometry of left invarint-metrics on Heisenberg groups. Also, some geometric properties of left-invarainat Randers metrics will be studied.

Interstellar gas passing through the solar system may effect the interplanetary gas, planetary atmospheres and satellite orbits. Interaction of the interstellar and interplanetary gases is considered; a solar system corona may be formed.

This paper aims to present the control laws to be used in the control of pendular motion on tethered satellite systems in space during orbiting by using a nonlinear design technique.

This work presents both physical and mathematical models represented in a circular orbit. Euler equation of the rigid body is applied under reasonable assumption so as to form the equations of pendular motion. These equations are then used to develop the control laws using a nonlinear design technique. The control laws are required to drive the in-plane angles and out-of-plane angles of the pendular motion to the required trajectories. Simulations are then conducted to study the control results.

Simulation results show that the control laws in both plane angles of motions considered are able to move the pendular motion to the required trajectory. It was also eminent that a lot of effort is required in the case of the reference trajectory that corresponds to the constant inside-plane. To control the pendular motion of the plane, one requires an extended period of time and it should be controlled within a reasonable range. In the outside-of-plane pendular motion, minimal or no effort is required for the control. The reason is that the trajectory is natural planar.

This research is expected to provide a dynamic control strategy for all tethered satellite space systems.

The research proposes a combined dynamic method for the purpose of improving the control of all types of tether satellites.

The purpose of this research was to analyze application effects of the stable frozen orbit conditions in the spacecraft Orbital Maintenance Maneuver (OMM) reduction.

One challenge in implementing these motions is maintaining the relations as it experiences orbital perturbations (zonal harmonics), most notably due to the non-spherical Earth. A natural phenomenon exists called a frozen orbit, for which the orbital elements: argument of perigee (ω) and eccentricity (e) remain virtually fixed over extended periods of time.

Simulation results show that, using stable frozen orbit condition results in considerable propellant saving, decreased OMM, increase of accuracy position errors and thus performance improvement of the spacecraft for orbiter mission is preferable. So, from among three proposed theories, the Brouwer–Hori theory has provided better accuracy and more stable conditions in the frozen orbit.

Simulation algorithm has been achieved to solve this problem by extracting and combining the equations that govern the frozen conditions with the tangential forces (ΔV) equations for orbit correction.

In all studies with content of harmonic perturbation effects on the spacecraft motion dynamics, main goal is to obtain a solution for optimization of the operation process, so that overshadowed mission costs. The case studies about this aim, mostly to the trajectory parameters optimization by considering the vehicle orbital conditions under various control methods are formed. While in this regards, the intrinsic properties of stable Earth orbits and using them effectively is less than to analyse the problems is considered.