Analytical Quasi-Optimal Solution for the Problem on Turn Maneuver of an Arbitrary Solid with Arbitrary Doundary Conditions

Abstract

The problem of energy-optimal turn maneuver of a solid having arbitrary dynamic configuration is considered within the framework of the quaternion formulation with arbitrary boundary conditions and without restrictions imposed on the control function. This turn maneuver is performed in fixed time. In the class of generalized conical motions, the optimal turn maneuver problem has been modified. As a result, it is possible to obtain its analytical solution. The analytical solution of the modified problem can be considered as an approximate (quasi-optimal) solution of the traditional optimal turn maneuver problem. An algorithm for the quasi-optimal turn maneuver of a solid is given. Given numerical examples illustrate that the solution of the modified problem is a close approximation for the solution of the traditional problem on the optimal turn maneuver of a solid. In addition, the examples show that the kinematic characteristics of the optimal motion in the traditional problem (attitude quaternion and angular velocity vector) depend weakly on the dynamic configuration of a solid and are mainly determined by the boundary conditions of the problem (anyway, for ϕ≥ π/2 where ϕ is the Euler angle). The weak dependence of the kinematic characteristics of the optimal motion of a solid on its dynamic configuration guarantees the closeness of the solutions of the modified and traditional problems of optimal turn maneuver of a body with an arbitrary dynamic configuration.