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# Topic: Equation of motion

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 Equation of motion - Wikipedia, the free encyclopedia In physics, equations of motion are equations that describe the behavior of a system (e.g., the motion of a particle under an influence of a force) as a function of time. Sometimes the term refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler-Lagrange equations), and sometimes to the solutions to those equations. The equations that apply to bodies moving linearly (that is, one dimension) with uniform acceleration are presented below. en.wikipedia.org /wiki/Equation_of_motion   (503 words)

 Equations of Motion The equations of motion are valid only when acceleration is constant and motion is constrained to a straight line. Motion along a curved path may also be effectively one-dimensional if there is only one degree of freedom for the objects involved. The second equation of motion is a quadratic and solving it for time would introduce a lot of nastiness into the algebra. hypertextbook.com /physics/mechanics/motion-equations/index.shtml   (3750 words)

 Equation of motion for a particle: Newton’s 2nd law Equation of motion for a particle: Newton’s 2nd law Equations of motion in a rectangular coordinate system: In a rectangular coordinate system the equations of motion can be represented by three scalar equations: Equations of motion in normal and tangential (natural) coordinate systems: In a natural coordinate system the equations of motion can be represented by three scalar equations: em-ntserver.unl.edu /NEGAHBAN/EM373/note9/note.htm   (250 words)

 The equation of motion relative to moving axes   (Site not responding. Last check: 2007-11-02) The acceleration of a fluid element in the moving frame may then be different than in the unaccelerated frame, and the equation of motion in the accelerated frame must be modified. This expression may be equated to the local force per unit mass of fluid to give the equation of motion in the rotating frame. The equation of motion of a fluid in a moving frame is therefore identical in form to that in an absolute frame provided we suppose that the fictitious body force grus.berkeley.edu /~jrg/ay202/node66.html   (504 words)

 Description of Motion   (Site not responding. Last check: 2007-11-02) Motion is described in terms of displacement (x), time (t), velocity (v), and acceleration (a). The case of motion in one dimension (one direction) is a good starting point for the description of motion. The motion equations represent a complete set of equations for constant acceleration motion, but in certain types of problems, intermediate results must be calculated before proceeding to the final calculation. hyperphysics.phy-astr.gsu.edu /Hbase/mot.html   (580 words)

 Equation of motion of an undamped and undriven pendulum Equation of motion of an undamped and undriven pendulum Although the equation of motion is derived only for a mathematical pendulum (where all the mass is concentrated in one point), it is also true for a physical pendulum with distributed mass. The equation of motion is a second-order differential equation (due to the second derivative of the angle monet.physik.unibas.ch /~elmer/pendulum/eqm1.htm   (465 words)

 MOTION IN TWO DIMENSIONS   (Site not responding. Last check: 2007-11-02) In projectile motion, the horizontal and the vertical components of the motion are treated separately. Its vertical motion is affected by the acceleration due to gravity. Motion information is given allowing one to calculate to speed and angle with which the object leaves the edge of the cliff. www.ship.edu /~sagoul/motion_in_two_dimensions.htm   (3524 words)

 The Equations of Motion   (Site not responding. Last check: 2007-11-02) The motion of the Earth around the sun is governed by the laws of circular motion but the positions and speeds of objects moving in a straight line can also be modelled mathematically. The motion of this object is represented by the graph shown in Fig.2. The straight-line nature of the graph in Fig.2 can be explained in terms of the first equation of motion, where the gradient of the line indicates the acceleration and the intercept on the y-axis gives the initial speed. www.crocodile-clips.com /absorb/AP5/sample/010104.html   (2040 words)

 #1 Site For Learning Science The second equation of motion is derived from the definition of average velocity. This equation is useful in calculating the distance traveled by a body if the initial velocity, acceleration and time are known. Motion of bodies can be calculated from the three equations of motions. home.att.net /~cat4a/equations_motion-II.htm   (408 words)

 Calculating the Equation of Motion Even though the parameterized orbits in equation (3.21) are different from the paths from Hamilton's principle, they behave similarly in the action A from equation (3.1). Note that the second term in equation (3.26) cancel the first in the limit of a homogeneous mass distribution. I close this section by noting that the boundary conditions in equation (3.27) can be arbitrary and are not restricted to the form needed by the AVP, since they were only used to remove the integrated part in equation (3.25). trond.hjorteland.com /thesis/node21.html   (577 words)

 Highbeam Encyclopedia - Search Results for Equation of motion motion MOTION [motion] the change of position of one body with respect to another. If the direction of motion is also given, then the velocity of the body is determined; velocity is a vector quantity, having both magnitude and direction, while speed is a scalar He was noted for his researches on heat and on numerical equations. encyclopedia.com /SearchResults.aspx?Q=Equation+of+motion&StartAt=11   (643 words)

 Semiclassical Theory: Dynamic Behavior of Quantum Systems In this picture, the appropriate equation of motion is one describing the motion or evolution of linear operators (dynamic variables) -- viz. Using a version of Equation [ II-3 ] we obtain the equation of motion for the state in the interaction picture -- viz. The equation of motion for the density operator is easily determined from the Schrödinger equation -- i.e. people.deas.harvard.edu /~jones/ap216/lectures/ls_2/ls2_u2/ls2_unit_2.html   (1077 words)

 Motion (physics) - Wikipedia, the free encyclopedia In physics, motion means a continuous change in the position of a body relative to a reference point, as measured by a particular observer in a particular frame of reference. Whereas Newton's laws of motion assumed absolute values of space and time in the equations of motion, the model of Einstein and Poincaré, now called the special theory of relativity, assumed values for these concepts with arbitrary zero points. In the newtonian model, because motion is defined as the proportion of space to time, these concepts are prior to motion, just as the concept of motion itself is prior to force. en.wikipedia.org /wiki/Motion_(physics)   (381 words)

 New Page 1 The equation of motion can be derived from Lagrange’s equations. When expressed in geometric terms using the metric tensor the classical equation of motion for zero force motion has the form of the geodesic equation. The equations of motion may be obtained through the use of Lagrange’s equations www.geocities.com /physics_world/mech/geometric_eof.htm   (263 words)

 Kepler's Equation of Elliptical Motion The geometric equation for an ellipse is quite simple; most high-school students are exposed to conic sections and their features. The position of a body in elliptical motion is usually found by way of an intermediate property: the eccentric anomaly, E (refer to the diagram below). Given an ellipse with semi-minor axis b and semi-major axis a, a circle of radius a is superposed upon the ellipse. www.akiti.ca /KeplerEquation.html   (882 words)

 The momentum equation in integral form   (Site not responding. Last check: 2007-11-02) Many fluid dynamics problems require the use of the equation of motion in differential form. Occasionally, it is useful to have an integral relation specifying the momentum balance for certain regions of the fluid. The remaining volume integral, on the LHS, which normally prevents use of the integral relation, is zero in the case of steady motion. grus.berkeley.edu /~jrg/ay202/node65.html   (260 words)

 Lagrange equation of motion question A smooth wire is bent into the form of a helix the equations of which, in cylindrical coordinates, are z=a*beta and r=b, in which a and b are constants. By means of Lagrange’s equations find the motion of a bead which is free to slide on the wire. Once you have the equation of motion use F = dr/dt in vector form and that will give you the total force on the particle. www.physicsforums.com /showthread.php?p=169017   (1119 words)

 Quantum Mechanical Langevin Equations With this equation it is possible to calculate the diffusion coefficients from the drift coefficients, provided one can independently calculate the equation of motion for The equation of motion for the laser field operator in a frame rotating at the laser frequency [6] In the classical Langevin theory of Browian motion, the equation of motion for drift velocity of a particle suspended in a liquid is given by people.deas.harvard.edu /~jones/ap216/lectures/ls_3/ls3_u7/ls3_unit_7.html   (1260 words)

 RaceReportsNet Report In this article, I present the equation of motion for inline skating, sometimes called the power equation, and show how it can be applied to determine the wheel configuration with the best roll independent of skater ability and technique. The power equation has been studied extensively in bicycling and in fact, some of the results presented here will be put into the context of this discipline. The equation of motion is solved with real-world measurements of the rolling resistance, the aerodynamic drag, and the moment of inertia of the wheels. www.racereports.net /ReportDetail.asp?Race=379   (416 words)

 GRAPHING MOTION This is the second equation of motion in a straight line. The three equations allow us to calculate the time, displacement, velocities and acceleration from given written information without the use of graphs although all of these can be related back to the graphs. Each part is a separate motion in the straight line and must have the equations applied to them separately. www.launc.tased.edu.au /online/sciences/PhysSci/done/kinetics/grap_eqn/Grmotion.htm   (631 words)

 Equations of Motion First, the equation of motion for the undamped and undriven pendulum will be derived. A bit more complicated is the derivation of the equation of motion for various damped and driven pendula. In physical textbooks quite often only the linearized equation of motions are discussed. monet.physik.unibas.ch /~elmer/pendulum/eqm.htm   (140 words)

 Equation of motion for nonequilibrium Green functions   (Site not responding. Last check: 2007-11-02) The equation of motion for nonequilibrium Green functions is derived within the framework of the Schwinger and Keldysh formalism of perturbation expansion. In the present work, the exact expression of singular terms is found in the equation of motion from the time-looped perturbation theory in which the adiabatic initial condition is implied. On the basis of this equation of motion, the procedure of a nonperturbative solution is outlined and potential applications are briefly discussed. stacks.iop.org /0953-8984/11/1511   (315 words)

 The Equation of Motion for n Charged Particles The equation of motion for a single, charged particle with periodic motion is Given no knowledge of past motions, however, a precise determination of the initial conditions (particularly of E(r,0) and B(r,0)) may not be feasible. The equations in this article specify a priori what the driving force must be in such cases, and what patterns of radiation can be expected. www.maxwellsociety.net /PhysicsCorner/InteractingParticles/nInteractingParticles/nChargedParticles.html   (1409 words)

 Appendices: Integrals of Motion The most familiar integrals of motion are energy and angular momentum. is both true and derivable from the equation of motion. We'll focus, first, on the right-hand-side of the equation of motion. www.phys.lsu.edu /astro/H_Book.current/Appendices/Integrals/integrals.of.motion.shtml   (444 words)

 The Damped Harmonic Motion   (Site not responding. Last check: 2007-11-02) A mass fixed to a spring and sliding on a plane is an example of a damped harmonic oscillator. It is a linear differential equation that may easily be checked, similar to the case of the nondamped harmonic oscillator (see equations (3), (4)). To solve this differential equation, we first have to look for two linear independent solutions x1(t) and x2(t), and then obtain the most general solution of the differential equation by an arbitrary choice of the coefficients A and B. physicsofmotion.com   (304 words)

 Solving the differential equation of motion Exercise 3: Write a code to integrate the equation of motion for SHM (equation 2) using the Euler method. We are in a position to look at the stability of our solution for the motion of the pendulum if we follow the motion for a much longer time t=3600 seconds, with dt=0.01. Exercise 8: For the simple harmonic motion pendulum, we have chosen the units so that one cycle or period is 1 second. www.dur.ac.uk /3h.physics/projects/fin_amp/node4.html   (842 words)

 Newton's Equation of Motion   (Site not responding. Last check: 2007-11-02) That this equation is really a second order differential equation in time, t, can be understood from the fact that acceleration is the derivative of the velocity, v, to time and velocity is the derivative of position, u, to time, viz. To find this solution in the case that an analytical solution is difficult, one can solve the second order differential equation in a numerical fashion by numerical integration. Thus armed with these two values and the equation of motion, one may numerically determine the trajectory of particles. chemistry.clemson.edu /ChemDocs/marcusgroup/software/CONCEPT/QMA/FMA/FMA.HTM   (524 words)

 Derive the equation of motion   (Site not responding. Last check: 2007-11-02) The equation of motion (E of M) of a system is an equation which expresses the fundamental laws of motion in terms of only (a) the degrees of freedom, (b) derivatives of the degrees of freedom, and (c) constants characterizing the system. In the example of the SHO, the fundamental law of motion is Newton's law. and, thereby, derive the equation of motion for the SHO, people.ccmr.cornell.edu /~muchomas/P214/Notes/SHM/node10.html   (192 words)

 Motion in oscillating fields Thus, the equation of motion for the centre of oscillation reduces to is conserved by the equation of motion (161). Thus, the force on the centre of oscillation originates in a transfer of energy from the oscillatory motion to the average motion. farside.ph.utexas.edu /~rfitzp/teaching/plasma/lectures/node26.html   (412 words)

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