China
Africa
Explore chapters and articles related to this topic
Canonical Equations of Celestial Mechanics
Published in G.A. Gurzadyan, Theory of Interplanetary Flights, 2020
The d’Alembert principle states that the external forces X, Y, and Z and the forces of inertia mx¨, y¨, and z¨ must always be in equilibrium. Strictly speaking, this principle represents nothing other than Newton’s third law: the action is equal to its reaction. However, the d’Alembert principle’s merit is in the fact of the serious involvement of this principle in the dynamics, thus reducing the problem of dynamics to a simple problem of statics. Below we will examine several examples of application of Lagrange equations to the problems of celestial mechanics.
N
Published in Carl W. Hall, Laws and Models, 2018
constant velocity, is proportional to the shear of the fluid motion at that position. Mathematically: = u/z where = shear = viscosity, constant of proportionality u = velocity u/z = velocity gradient z = half distance between plates Keywords: dynamics, fluid, friction, shear, velocity NEWTON, Sir Isaac, 1642-1727, English philosopher and mathematician Source: Gray, G. W. 1972. See also DARCY NEWTONIAN PARTICLE LAWS 1. A particle of mass, m, acted on by a resultant force, has an acceleration, F = ma. 2. The idea of action-reaction indicating that, when one particles exerts force on another, the other particle exerts on the one a colinear force equal in magnitude but oppositely directed. 3. A body, a system of particles, acted upon by force is in equilibrium when its constituent particles are in equilibrium. An internal force is exerted by one particle on another particle in the body. An external force is exerted on a particle or body by a particle not of the body. Keywords: acceleration, action-reaction, body, force, mass, particle NEWTON, Sir Isaac, 1642-1727, English philosopher and mathematician Source: Parker, S. P. 1992. See also other NEWTON LAWS NEWTON INERTIAL FORCE GROUP OR NUMBER, Nl A dimensionless group used in agitation relating the imposed force divided by the inertial force: Nl = F/ V2L2 where F V L = = = = imposed force mass density velocity characteristic length
Structural Mechanics Fundamentals
Published in Colin H. Hansen, Foundations of Vibroacoustics, 2018
The principle of virtual work states that if and only if, for any arbitrary virtual displacement, δr, the virtual work, δW = 0, under the action of the forces, Fi, the particle is in equilibrium. For non-zero δr, Equation (2.11) shows that either δr is perpendicular to ΣFi or ΣFi = 0. Since Equation (2.11) must hold for any δr, the first possibility is ruled out and ΣFi = 0. Thus, for a particle to be in equilibrium: () δW=F⋅δr=0
Performer interaction and expectation with live algorithms: experiences with Zamyatin
Published in Digital Creativity, 2018
In interview, Houle describes his experience playing with Zamyatin, referencing his general philosophy of working with interactive music systems: A programmer, or composer/creator of a machine needs to have a very clear musical vision that encompasses a deep understanding of all the parameters involved in a satisfying musical experience. I am talking about a visceral experience, where the music affects the senses in a very ‘physical’ and ‘emotional’ way.Interaction implies a two-way, action/reaction principle. If the system only reacts to an action without ever anticipating one, or by ever generating an action of its own, you end up with musical failure, as there is too much inequity at the participatory level. You can forget about what or who you are performing with, if the situation meets one's idea of what constitutes a satisfying musical experience.