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Ramy Rashad

My personal website showcasing my research works putting energy and geometry back in robotics!

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Nonlinear Elasticity
Geometric Modeling

Nonlinear Elasticity

Posted on: July 24, 2023August 11, 2023

Research Overview Identifying the underlying structure of partial differential equations is a fundamental topic in modern treatments of continuum mechanics and field theories in general. Not only does […]

Fourier-Navier-Stokes equations
Geometric Modeling

Fourier-Navier-Stokes equations

Posted on: October 26, 2022August 17, 2023

Research Overview In this paper, we present a comprehensive description of thermodynamics in a differential geometric setting for a general non-relativistic continuum mechanical system. In order to deal […]

Fluid-Structure-Interaction
Geometric Modeling

Fluid-Structure-Interaction

Posted on: February 17, 2022August 17, 2023

Research Overview The goal of this work is to extend the existing port-Hamiltonian theory of open distributed parameter systems on fixed spatial domains to the practically relevant case […]

Multirotor UAVs
Geometric Modeling

Multirotor UAVs

Posted on: November 25, 2021August 11, 2023

Research Overview In this paper we present a systematic modeling framework for generic MAVs that encompasses a wide spectrum of possible designs. We assume the MAVs are driven […]

Navier-Stokes Equations
Geometric Modeling

Navier-Stokes Equations

Posted on: April 26, 2021August 12, 2023

Research Overview The specific aim of this work is to extend the port-Hamiltonian formulation of ideal compressible fluids (Euler equations) to Newtonian viscous fluids (Navier–Stokes equations). The way […]

Ideal Fluid Flow
Geometric Modeling

Ideal Fluid Flow

Posted on: March 5, 2021August 12, 2023

Research Overview Fluid mechanics has been studied in the literature using both the Lagrangian and Hamiltonian formalism. In the classical Hamiltonian theory for fluid dynamical systems, a fundamental […]

Rigid Body Dynamics
Geometric Modeling

Rigid Body Dynamics

Posted on: January 21, 2021August 12, 2023

This work has been published as Ch.4 of my PhD thesis. The study of rigid body modeling is central to the mathematical theories of robotics. The topic of […]

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