Euler's Equations of Motion

1878 ◽  
Vol 1 (4) ◽  
pp. 387
Author(s):  
James Loudon
Keyword(s):  
Equations Of Motion ◽  
Euler’S Equations ◽  
Euler's Equations

Complete Six-Degrees-of-Freedom Nonlinear Ship Rolling Motion

1994 ◽  
Vol 116 (4) ◽  
pp. 191-201 ◽  
Author(s):  
M. Taz Ul Mulk ◽  
J. Falzarano
Keyword(s):  
Degrees Of Freedom ◽  
Second Harmonic ◽  
Equations Of Motion ◽  
Path Following ◽  
Euler Angle ◽  
Moment Curve ◽  
Six Degrees Of Freedom ◽  
Euler’S Equations ◽  
Euler's Equations ◽  
Asymmetric Nonlinearity

The emphasis of this paper is on nonlinear ship roll motion, because roll is the most critical ship motion of all six modes of motion. However, coupling between roll and the other modes of motion may be important and substantially affect the roll. Therefore, the complete six-degrees-of-freedom Euler’s equations of motion are studied. In previous work (Falzarano et al., 1990, 1991), roll linearly coupled to sway and yaw was studied. Continuing in this direction, this work extends that analysis to consider the dynamically more exact six-degrees-of-freedom Euler’s equations of motion and associated Euler angle kinematics. A combination of numerical path-following techniques and numerical integrations are utilized to study the steady-state response determined using this more exact modeling. The hydrodynamic forces are: linear frequency-dependent added-mass, damping, and wave-exciting, which are varied on a frequency-by-frequency basis. The linearized GM approximation to the roll-restoring moment is replaced with the nonlinear roll-restoring moment curve GZ(φ), and the linear roll wave damping is supplemented by an empirically derived linear and nonlinear viscous damping. A particularly interesting aspect of this modeling is the asymmetric nonlinearity associated with the heave and pitch hydrostatics. This asymmetric nonlinearity results in distinctive “dynamic bias,” i.e., a nonzero mean in heave and pitch time histories for a zero mean periodic forcing, and a substantial second harmonic. A Fourier analysis of the nonlinear response indicates that the harmonic response is similar to the linear motion response.

scholarly journals Bumpy Spin-Down of Anomalous X-Ray Pulsars: The Link with Magnetars

2000 ◽  
Vol 177 ◽  
pp. 691-694
Author(s):  
A. Melatos
Keyword(s):  
Neutron Star ◽  
Gamma Ray ◽  
Equations Of Motion ◽  
Recurrence Time ◽  
Statistical Relation ◽  
Dipole Radiation ◽  
X Ray ◽  
Euler’S Equations ◽  
Euler's Equations

AbstractIt is argued that bumps in the timing histories Ω(t) of the anomalous X-ray pulsars (AXPs) IE 1048.1-5937 and IE 2259+586 are the signature of a magnetar undergoing radiative precession, wherein the hydromagnetic deformation of the neutron star couples to an oscillating component of the vacuum-dipole radiation torque to produce an anharmonic wobble with periodτpr∼ 10 yr. An analysis of Euler’s equations of motion for a biaxial magnet reproduces the amplitude and recurrence time of the bumps for IE 1048.1-5937 and IE 2259+586, predicts Ω(t) for the next 20 years for both objects, and predicts a testable statistical relation betweendΩ/dtandτprfor the AXP population overall. Radiative precession of soft gamma-ray repeaters is also discussed, together with implications for the internal (e.g. viscosity) and magnetospheric (e.g.e+e−pair currents) properties of magnetars.

A Dynamic Analysis of a Spatial Mechanism With a Passive Degree of Freedom

1989 ◽  
Vol 111 (2) ◽  
pp. 238-242 ◽  
Author(s):  
C. H. Suh ◽  
H. Y. Kang
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Degree Of Freedom ◽  
Displacement Velocity ◽  
Spatial Mechanism ◽  
Spatial Mechanisms ◽  
Euler’S Equations ◽  
Kinematic Method ◽  
Euler's Equations

A method is developed for kinematic and dynamic analysis of a spatial mechanisms that has one or more links with a passive degree of freedom. The Sphere-Sphere (SS) link, the most commonly known link having a passive degree of freedom, is investigated to develop in detail displacement, velocity, and acceleration matrices for complete kinematics. The dynamic analysis of the RSSR mechanism is presented as an example, using the developed kinematic method for SS links and Euler’s equations of motion.

Kinematics and dynamics of a parallel manipulator with a new architecture

Robotica ◽  
2000 ◽  
Vol 18 (5) ◽  
pp. 535-543 ◽  
Author(s):  
A. Fattah ◽  
G. Kasaei
Keyword(s):  
Parallel Manipulator ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Orthogonal Complement ◽  
Flight Simulator ◽  
Kinematics And Dynamics ◽  
Dynamical Equations ◽  
Euler’S Equations ◽  
Euler's Equations ◽  
Moving Platform

In this paper, the kinematics and dynamics of a parallel manipulator with a new architecture supposed to be used as a moving mechanism in a flight simulator project is studied. This manipulator with three independent degrees of freedom consists of a moving platform connected to a based platform by means of three legs. Kinematic solutions for this manipulator at position, velocity and acceleration levels are obtained. Moreover, the dynamical equations of motion of the manipulator are determined using Newton-Euler's equations and applying the natural orthogonal complement (NOC) method. Using kinematics and dynamics and also performing simulation for different manoeuvres of moving platform, the motion and the actuator forces of the legs are obtained.

scholarly journals Convergence of Vortex Methods for Euler's Equations

1978 ◽  
Vol 32 (143) ◽  
pp. 791 ◽  
Author(s):  
Ole Hald ◽  
Vincenza Mauceri Del Prete
Keyword(s):  
Vortex Methods ◽  
Euler’S Equations ◽  
Euler's Equations

A physics-based turbocharger model for automotive diesel engine control applications

2018 ◽  
Vol 233 (7) ◽  
pp. 1667-1686 ◽  
Author(s):  
Kang Song ◽  
Devesh Upadhyay ◽  
Hui Xie
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Turbine Rotor ◽  
Variable Geometry ◽  
Gas Velocity ◽  
Euler’S Equations ◽  
Variable Geometry Turbine ◽  
Euler's Equations ◽  
Compressor Power

Control-oriented models of turbocharger processes such as the compressor mass flow rate, the compressor power, and the variable geometry turbine power are presented. In a departure from approaches that rely on ad hoc empirical relationships and/or supplier provided performance maps, models based on turbomachinery physics and known geometries are attempted. The compressor power model is developed using Euler’s equations of turbomachinery, where the gas velocity exiting the rotor is estimated from an empirically identified correlation for the ratio between the radial and tangential components of the gas velocity. The compressor mass flow rate is modeled based on mass conservation, by approximating the compressor as an adiabatic converging-diverging nozzle with compressible fluid driven by external work input from the compressor wheel. The variable geometry turbine power is developed with Euler’s equations, where the turbine exit swirl and the gas acceleration in the vaneless space are neglected. The gas flow direction into the turbine rotor is assumed to align with the orientation of the variable geometry turbine vane. The gas exit velocity is calculated, similar to the compressor, based on an empirical model for the ratio between the turbine rotor inlet and exit velocities. A power loss model is also proposed that allows proper accounting of power transfer between the turbine and compressor. Model validation against experimental data is presented.

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