Bhanu Kumar's research while affiliated with Georgia Institute of Technology and other places
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Publications (6)
![Schematic of crossing gaps during ω\documentclass[12pt]{minimal}...](publication/357576445/figure/fig1/AS:1129011749105665@1646188785287/Schematic-of-crossing-gaps-during-odocumentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Continuation of ε=0.0094\documentclass[12pt]{minimal}...](publication/357576445/figure/fig3/AS:1129011749109763@1646188785329/Continuation-of-e00094documentclass12ptminimal-usepackageamsmath_Q320.jpg)
![Continuation of ε=0.0094\documentclass[12pt]{minimal}...](publication/357576445/figure/fig4/AS:1129011749093381@1646188785364/Continuation-of-e00094documentclass12ptminimal-usepackageamsmath_Q320.jpg)
When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable periodic orbits break up into whiskered tori, with most tori persisting into the perturbed system. In this study, we (1) develop a quasi-Newton method which simultaneously solves for the tori and their center, stable, and unstable directions; (...
When the planar circular restricted 3-body problem is periodically perturbed, most unstable periodic orbits become invariant tori. However, 2D Poincar\'e sections no longer work to find their manifolds' intersections; new methods are needed. In this study, we first review a method of restricting the intersection search to only certain manifold subs...
Many unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equations of motion. In this study, we compute tori corresponding to exterior Jupiter-Europa and interior Jupiter-Ganymede PCRTBP resonant periodic orbits in a concentric circular restricted 4-bod...
In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approxi...
When the planar circular restricted 3-body problem (RTBP) is periodically perturbed, families of unstable resonant periodic orbits break up into whiskered tori, with most tori persisting into the perturbed system. In this study, we 1) develop a quasi-Newton method which simultaneously solves for the tori and their center, stable, and unstable direc...
In recent years, stable and unstable manifolds of invariant objects (such as libration points and periodic orbits) have been increasingly recognized as an efficient tool for designing transfer trajectories in space missions. However, most methods currently used in mission design rely on using eigenvectors of the linearized dynamics as local approxi...
Citations
... The results are stated following a posteriori formulation: if there is an approximate solution of the invariance equation satisfying some non-degeneracy conditions, then there exist a true solution nearby. Rather rapidly, the parameterization method lead to a plethora of rigorous results [10,14,23,27,35,39] and numerical explorations [11,9,13,28,33,38], in different contexts, to name a few. See [29] for a survey. ...
![[object Object]](https://i1.rgstatic.net/ii/profile.image/301683432280067-1448938343898_Q64/Rodney-Anderson-3.jpg)
... They are allowing to develop high order perturbative expansions in new situations. These new tehcniques are expected to have an impact in the design of space missions during the next years (Chen et al., 2020;Kumar et al., 2021). Another problem of high interest in astrodynamics is the dynamics of space debris , which has become very important for space navigation. ...
Reference: Computational Methods in Perturbation Theory
