Impulse (physics)

Summary

In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. If the initial momentum of an object is p1, and a subsequent momentum is p2, the object has received an impulse J: \vec{J}=\vec{p_2} - \vec{p_1}. Momentum is a vector quantity, so impulse is also a vector quantity. Newton’s second law of motion states that the rate of change of momentum of an object is equal to the resultant force F acting on the object: \vec{F}=\frac{\vec{p_2} - \vec{p_1}}{\Delta t}, so the impulse J delivered by a steady force F acting for time Δt is: \vec{J}=\vec{F} \Delta t. The impulse delivered by a varying force is the integral of the force F with respect to time: \vec{J} = \int \vec{F} ,\mathrm{d}t. The SI unit of impulse is the newton second (N⋅s), and the dimensionally equ

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Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves

Alexandre Caboussat, Marco Picasso

A numerical method for the solution to the density-dependent incompressible Navier-Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid phases together with an additional vacuum phase separated with a free surface. It is based on a volume-of-fluid approach involving N indicator functions (one per phase, identified by its density) that guarantees mass conservation within each phase. An additional indicator function for the whole liquid domain allows to treat boundary conditions at the interface between the liquid domain and a vacuum. The system of partial differential equations is solved by implicit operator splitting at each time step: first, transport equations are solved by a forward characteristics method on a fine Cartesian grid to predict the new location of each liquid phase; second, a generalized Stokes problem with a density-dependent viscosity is solved with a FEM on a coarser mesh of the liquid domain. A novel algorithm ensuring the maximum principle and limiting the numerical diffusion for the transport of the N phases is validated on benchmark flows. Then, we focus on a novel application and compare the numerical and physical simulations of impulse waves, that is, waves generated at the free surface of a water basin initially at rest after the impact of a denser phase. A particularly useful application in hydraulic engineering is to predict the effects of a landslide-generated impulse wave in a reservoir. Copyright (c) 2014 John Wiley & Sons, Ltd.

Wiley-Blackwell2014

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Micro Aerial Vehicles (MAVs) with perching capabilities can be used to efficiently place sensors in aloft locations. A major challenge for perching is to build a lightweight mechanism that can be easily mounted on a MAV, allowing it to perch (attach and detach on command) to walls of different materials. To date, only very few systems have been proposed that aim at enabling MAVs with perching capabilities. Typically, these solutions either require a delicate dynamic flight maneuver in front of the wall or expose the MAV to very high impact forces when colliding head-first with the wall. In this article, we propose a 4.6g perching mechanism that allows MAVs to perch on walls of natural and man- made materials such as trees and painted concrete facades of buildings. To do this, no control for the MAV is needed other than flying head-first into the wall. The mechanism is designed to translate the impact impulse into a snapping movement that sticks small needles into the surface and uses a small electric motor to detach from the wall and recharge the mechanism for the next perching sequence. Based on this principle, it damps the impact forces that act on the platform to avoid damage of the MAV. We performed 110 sequential perches on a variety of substrates with a success rate of 100%. The main contributions of this article are (i) the evaluation of different designs of perching, (ii) the description and formal modeling of a novel perching mechanism, and (iii) the demonstration and characterization of a functional prototype on a microglider.

2010

An Evaluation of Moreau’s time-stepping scheme for the simulation of a legged robot

Roland Siegwart

A state-of-the-art simulation technique that solves the equations of motion together with the set-valued contact and impulse laws by the time-stepping scheme of Moreau is introduced to the legged robotics community. An analysis is given that shows which of the many variations of the method fits best to legged robots. Two different methods to solve the discretized normal cone inclusions are compared: the projected over-relaxed Jacobi and Gauss-Seidel iteration. The methods are evaluated for an electrically-driven quadrupedal robot in terms of robustness, accuracy, speed and ease of use. Furthermore, the dependence of the simulation speed on the choice of the generalized coordinates is examined. The proposed technique is implemented in C++ and compared to a fast and simple approach based on compliant contact models. In conclusion, the introduced method with hard contacts is very beneficial for the simulation of legged robots.

2014