Research Interests
Fluid Mechanics, Aeroelasticity and Fluid-Structure Interaction, Dynamics and Vibrations, Robotics & Controls
Theoretical Fluid Mechanics (vortex dynamics, specifically the dynamics of singular coherent vortical structures such as point vortices, vortex filaments and vortex patches), Dynamical Systems (geometric mechanics, the study of Lagrangian and Hamiltonian systems and of the role that geometry plays in the behavior of nonlinear systems), Nonlinear Control Theory (optimal control theory and geometric control theory and their applications to finite-dimensional systems)
Current Projects
- Modeling, simulation and understanding of the complex nonlinear phenomena in the dynamics and control of coupled fluid-solid systems. The focus is on inviscid, incompressible flows–endowed with vorticity–dynamically interacting with rigid and deformable solids. Hamiltonian models of such problems are being currently investigated. Applications are to biomimetic locomotion and biological swimming problems (such as fish swimming and bird flight).
- Hamiltonian and dissipative models for interacting vortex structures in incompressible flows. Recent modeling work incorporates dissipative effects, which respect Navier-Stokes symmetry properties, into Hamiltonian models of singular coherent vortical structures such as point vortices and vortex filaments.
- Optimal control problems involving ideal fluids or/and rigid bodies: applications, mainly of Pontryagin’s Maximum Principle along with ideas in geometric control, to different problems.
Book
Dynamically Coupled Rigid Body-Fluid Flow Systems, Springer, 2021.https://link.springer.com/book/10.1007/978-3-030-82646-8
Recent Publications
Journal Publications
- Application of Kirchhoff’s equations of motion to the dynamically coupled system of a rigid body with a completely-liquid-filled cavity, B. N. Shashikanth, Mathematics and Mechanics of Solids, 2023 (first published online February 17, 2023). https://doi.org/10.1177/10812865231151391
- The centroid-deformation decomposition for buoyant vortex patch motion, B. N. Shashikanth and R. Kidambi, Regul. Chaot. Dyn., vol. 26, pp. 577–599, 2021. https://doi.org/10.1134/S1560354721060010 (pdf)
- Poisson brackets for the dynamically coupled system of a free boundary and a neutrally buoyant rigid body in a body-fixed frame, B. N. Shashikanth, Journal of Geometric Mechanics, vol. 12(1), pp. 25-52, 2020. (pdf)
- Reconstruction phases in the planar three- and four-vortex problems, A. Hernández-Garduño and B. N. Shashikanth, Nonlinearity, Vol. 31, pp. 783–814, 2018. (pdf)
- Kirchhoff’s equations of motion via a constrained Zakharov system, B. N. Shashikanth, Journal of Geometric Mechanics, vol. 8(4), pp.461–485, 2016. (pdf)
- Non-invasive determination of external forces in vortex-pair-cylinder interactions, D. Hartmann, W. Schroeder, and B. N. Shashikanth, Physics of Fluids , vol. 24, 061903, 27 pages, 2012. (pdf)
