Approximate closed-form solutions of realistic true proportional navigation guidance using the Adomian decomposition method

Approximate closed-form solutions of the non-linear relative equations of motion of an interceptor pursuing a target under the realistic true proportional navigation (RTPN) guidance law are derived using the Adomian decomposition method in this article. In the literature, no study has been reported on derivation of explicit time-series solutions in closed form of the nonlinear dynamic engagement equations under the RTPN guidance. The Adomian method provides an analytical approximation, requiring no linearization or direct integration of the non-linear terms. The complete derivation of the Adomian polynomials for the analysis of the dynamics of engagement under RTPN guidance is presented for deterministic ideal case, and non-ideal dynamics in the loop that comprises autopilot and actuator dynamics and target manoeuvre, as well as, for a stochastic case. Numerical results illustrate the applicability of the method.

Engagement of CF3 Group in N-H center dot center dot center dot F-C Hydrogen Bond in the Solution State: NMR Spectroscopy and MD Simulation Studies

Unambiguous evidence for the engagement of CF3 group in N-H center dot center dot center dot F-C hydrogen bond in a low polarity solvent, the first observation of its kind, is reported. The presence of such weak molecular interactions in the solution state is convincingly established by one and two-dimensional H-1, F-19, and natural abundant N-15 NMR spectroscopic studies. The strong and direct evidence is derived by the observation of through-space couplings, such as, (1h)J(FH), (1h)J(FN), and (2h)J(FF), where the spin polarization is transmitted through hydrogen bond. In an interesting example of a molecule containing two CF3 groups getting simultaneously involved in hydrogen bond, where hydrogen bond mediated couplings are not reflected in the NMR spectrum, F-19-F-19 NOESY experiment yielded confirmatory evidence. Significant deviations in the strengths of (1)J(NH), variable temperature, and the solvent induced perturbations yielded additional support. The NMR results are corroborated by both DFT calculations and MD simulations, where the quantitative information on different ways of involvement of fluorine in two and three centered hydrogen bonds, their percentage of occurrences, and geometries have been obtained. The hydrogen bond interaction energies have also been calculated.

Capturability of augmented proportional navigation (APN) guidance with nonlinear engagement dynamics

Proportional Navigation (PN) and its variants are widely used guidance philosophies. However, in the presence of target maneuver, PN guidance law is effective only for a restrictive set of initial geometries. To account for target maneuvers, the concept of Augmented Proportional Navigation (APN) guidance law was introduced and analyzed in a linearized interceptor-target engagement framework presented in literature. However, there is no work in the literature, that addresses the capturability performance of the APN guidance law in a nonlinear engagement framework. This paper presents such an analysis and obtains the conditions for capturability. It also shows that a shorter time of interception is obtained when APN is formulated in the nonlinear framework as proposed in this paper. Simulation results are given to support the theoretical findings.