Applying integrals of motion to the numerical solution of differential equations

A method is developed for using the integrals of systems of nonlinear, ordinary differential equations in a numerical integration process to control the local errors in these integrals and reduce the global errors of the solution. The method is general and can be applied to either scaler or vector integrals. A number of example problems, with accompanying numerical results, are used to verify the analysis and support the conjecture of global error reduction

On the use of approximate analytical solutions in solving optimum trajectory problems

Method for numerical solutions of nonlinear optimum trajectory problems using approximate analytic metho

Primer vector theory and applications

A method developed to compute two-body, optimal, N-impulse trajectories was presented. The necessary conditions established define the gradient structure of the primer vector and its derivative for any set of boundary conditions and any number of impulses. Inequality constraints, a conjugate gradient iterator technique, and the use of a penalty function were also discussed

Development of a method for optimal maneuver analysis of complex space missions

A system that allows mission planners to find optimal multiple-burn space trajectories easily is described. Previously developed methods with different gravity assumptions perform the optimization function. The power of these programs is extended by a method of costate estimation. A penalty function method of constraining coast arc times to be positive is included. The capability of the method is demonstrated by finding the optimal control for three different space missions. These include a shuttle abort-once-around mission and two- and three-burn geosynchronous satellite-placement missions

Protein prenylation and Hsp40 in thermotolerance of Plasmodium falciparum malaria parasites

During its complex life cycle, the malaria parasite survives dramatic environmental stresses, including large temperature shifts. Protein prenylation is required during asexual replication of Plasmodium falciparum, and the canonical heat shock protein 40 protein (HSP40; PF3D7_1437900) is posttranslationally modified with a 15-carbon farnesyl isoprenyl group. In other organisms, farnesylation of Hsp40 orthologs controls their localization and function in resisting environmental stress. In this work, we find that plastidial isopentenyl pyrophosphate (IPP) synthesis and protein farnesylation are required for malaria parasite survival after cold and heat shock. Furthermore, loss of HSP40 farnesylation alters its membrane attachment and interaction with proteins in essential pathways in the parasite. Together, this work reveals that farnesylation is essential for parasite survival during temperature stress. Farnesylation of HSP40 may promote thermotolerance by guiding distinct chaperone-client protein interactions

Duality properties of Gorringe-Leach equations

In the category of motions preserving the angular momentum's direction, Gorringe and Leach exhibited two classes of differential equations having elliptical orbits. After enlarging slightly these classes, we show that they are related by a duality correspondence of the Arnold-Vassiliev type. The specific associated conserved quantities (Laplace-Runge-Lenz vector and Fradkin-Jauch-Hill tensor) are then dual reflections one of the othe