Engineering topics
Publications and source records attributed to Jezewski, D..
An analytic solution to the two-body problem with a specific drag model is obtained. The model treats drag as a force proportional to the vector velocity and inversely proportional to the square of the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time-of-flight is expressed as a quadrature in the 'true anomaly'.
The two body problem was analyzed with a specific drag model. The model treats drag as a force proportional to the vector velocity and inversely proportional to the distance to the center of attraction. The solution is expressed in terms of known functions and is of a simple and compact form. The time of flight is expressed as a quadrature in the true anomaly. The results are: (1) development of a vector differential equation which allows analysis of an infinite number of gravitational and drag models; and (2) obtaining the solution of a linear differential equation using the inverse method of laplace transforms.
Prime vector theory is used in analyzing a set of linear relative-motion equations - the Clohessy-Wiltshire (C/W) equations - to determine the criteria and necessary conditions for an optimal N-impulse trajectory. The analysis develops the analytical criteria for improving a solution by: (1) moving any dependent or independent variable in the initial and/or final orbit, and (2) adding intermediate impulses. If these criteria are violated, the theory establishes a sufficient number of analytical equations. The subsequent satisfaction of these equations will result in the optimal position vectors and times of an N-impulse trajectory. The solution is examined for the specific boundary conditions of: (1) fixed-end conditions, two impulse, and time-open transfer; (2) an orbit-to-orbit transfer; and (3) a generalized renezvous problem.