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.

The Integrated Mission Simulator

SIMULATION ◽  
1964 ◽  
Vol 2 (2) ◽  
pp. R-9-R-23
Author(s):  
Edward E. Markson ◽  
John L. Stricker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Landing Site ◽  
Euler Angle ◽  
Space Mission ◽  
Six Degrees Of Freedom ◽  
Guidance And Control ◽  
Manned Space ◽  
And Control ◽  
Guidance Technique

Space mission simulator programs may be divided into two broad categories: (1) training tools (quali tative devices often simulating a continuous mission), and (2) laboratory tools (quantitative devices treating the mission in phases, each phase being programmed separately to obtain optimum scaling). This paper describes the development of an analog program capable of continuously simulating an entire lunar mission in six degrees of freedom with high resolu tion throughout. The reported work logically traces the program development through the equations of motion, the guidance and control equations, and the analog mechanization. The translation equations are de veloped using a modified form of Encke's method; two reference origins are utilized at the two points of primary interest—the landing site and the target vehicle—such that the displacements are approach ing a minimum in the regions where the highest reso lution is required. The variables are rescaled as this region is approached to obtain maximum accuracy. Relays, stepping switches and diode gates are used for rescaling and to re-reference origins. A particular Euler angle sequence is selected based on matrix validity criteria applied to the mission. A previously reported guidance technique is shown to be appli cable to all phases of the mission. It is concluded that the method demonstrated in this paper leads to minimum computer loading for simulating a manned space mission without program discontinuities. Supporting data include an analog- computed trajectory representative of a long-dura tion mission, which is compared in detail with a digital solution.

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.

Study on Motion Simulation of HOV

2013 ◽  
Vol 694-697 ◽  
pp. 158-162
Author(s):  
Feng Liu ◽  
Duan Feng Han
Keyword(s):  
Degrees Of Freedom ◽  
Hydrodynamic Force ◽  
Equations Of Motion ◽  
Control System Design ◽  
Motion Simulation ◽  
Six Degrees Of Freedom ◽  
Movement Performance ◽  
Motion Characteristics ◽  
Motor Effects ◽  
Important Basis

It will be to bear several forces when Human Occupied Vehicle (HOV) moves underwater, So the movement performance forecast and research becomes more difficult when HOV under environment disturbances,this paper regards a certain HOV as the research object,researches the HOV actual situation, the comprehensive consideration of the hydrodynamic force, gravity, propeller thrust, environmental interference force for HOV motor effects, establishes the six degrees of freedom equations of motion for HOV, several typical motion states are studied , finally the simulation work is carried out, the simulation results can reflect the HOV motion characteristics , provide important basis for HOV motion control system design.

A Three-Dimensional Dynamic Model for Determining the Equilibrium Configurations of Buoyantly Unstable Icebergs

1990 ◽  
Vol 112 (3) ◽  
pp. 253-262
Author(s):  
R. G. Jessup ◽  
S. Venkatesh
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Static Potential ◽  
Initial State ◽  
Model Simulations ◽  
Six Degrees Of Freedom ◽  
Equilibrium Configurations ◽  
Variation Range

This paper describes a dynamic model developed for the purpose of determining the final equilibrium configurations of buoyantly unstable icebergs. The model places no restrictions on the size, shape, or dimensionality of the iceberg, or on the variation range of the configuration coordinates. Furthermore, it includes all six degrees of freedom and is based on a Lagrangian formulation of the dynamic equations of motion. It can be used to advantage in those situations in which the iceberg has a complicated potential function and can acquire enough momentum and kinetic energy in the initial phase of its motion to make its final configuration uncertain on the basis of a static potential analysis. The behavior of the model is examined through several model simulations. The sensitivity of the final equilibrium position to the initial orientation and shape of the iceberg is clearly evident in the model simulations. Model simulations also show that when an iceberg is released from a nonequilibrium initial state, the time taken for it to settle down varies from about 40 s for a growler to nearly 400 s for a large iceberg. While these absolute times may change with better parameterization of the forces, the relative variations with iceberg size are likely to be preserved.

Imbalance Effects in Rotor Systems Under High Angular Accelerations

1994 ◽  
Author(s):  
R. D. Neilson ◽  
A. D. S. Barr ◽  
N. J. Blandford-Baker
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Angular Acceleration ◽  
Torsional Stiffness ◽  
Flexible Rotor ◽  
Disk System ◽  
Transient Vibration ◽  
Rotor Systems ◽  
Six Degrees Of Freedom ◽  
Transient Problems

To assess correctly the effects of transient vibration in a system with imbalance care is required in modelling the system. This is particularly true in cases of extreme imbalance e.g. a blade-off simulation in turbo-machinery. Generally, however, the imbalance is modelled as a simple mrΩ2 term applied when the blade is released but this does not include all possible terms. This paper presents the detailed equations of motion of a flexible rotor system with distributed imbalance. The equations are presented in a rotating coordinate system. The modelling includes coupling between the torsional, lateral and axial motions. A simpler model of a two disk system is then presented in fixed coordinates. The disks which can move laterally am connected by a massless shaft which has both lateral and torsional stiffness giving the system six degrees of freedom. An analysis is presented showing that the model is the same as the conventional model for steady state circular orbits. Results from a simplified blade-off simulation are then presented and compared to the standard mrΩ2 model. The conclusion drawn from these simulations is that the additional terms should be included for high angular acceleration transient problems.

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.

The Analysis of Motions of Semisubmersible Drilling Vessels in Waves

1970 ◽  
Vol 10 (03) ◽  
pp. 311-320 ◽  
Author(s):  
Ben G. Burke
Keyword(s):  
Mathematical Model ◽  
Test Data ◽  
Model Test ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Basic Principles ◽  
Six Degrees Of Freedom ◽  
Drilling Equipment ◽  
Wave Response ◽  
The Mathematical Model

Abstract A mathematical model was developed to compute the motions of semisubmersible drilling vessels in waves for a wide variety of semisubmersible configurations. The model was derived from a linear representation of motions, ocean waves, and forces. The semisubmersible is represented as a rigid space frame composed of a number of cylindrical members with arbitrary diameters, lengths and orientations. Forces on the semisubmersible are derived from anchorline properties, and hydrostatic hydrodynamic principles. A solution is obtained for motions in six degrees of freedom for a sinusoidal wave train of arbitrary height, period, direction and water depth. Results from the analysis of three semisubmersibles are compared with results from available model test data to verily the mathematical model. Introduction An accurate and complete representation of the response of a drilling vessel to waves is a valuable engineering tool for predicting vessel performance and designing drilling equipment. The performance and designing drilling equipment. The wave response for a floating vessel may be obtained to various degrees of accuracy from model tests or analytical means, as described by Barkley and Korvin-Kroukovsky and as applied by Bain. A review of the works cited shows that the evaluation of the wave response for a particular vessel requires considerable time and effort, either in model construction and testing or in computer programming and calculations. In order to reduce programming and calculations. In order to reduce the amount of time and effort required to evaluate a particular vessel, means were investigated to generalize and automate, on a digital computer, methods for evaluating wave response for vessels of arbitrary configuration. The mathematical model described in this paper is the result of such an investigation for semisubmersible-type drilling vessels. The paper presents a general description of the mathematical model and the basic principles and assumptions from which it was derived. The validity of the model is evaluated by comparing results of the analysis of three semisubmersibles with available model test data. MATHEMATICAL MODEL The mathematical model for calculating the motions of a semisubmersible in waves is derived from basic principles and empirical relationships in classical mechanics. All equations are derived for "small amplitude" waves and motions. The nonlinear equations that appear in the problem are replaced by "equivalent" linear equations in order to conform to the linear analysis method used in obtaining a solution. The model is implemented in a computer program that computes vessel response in all six degrees of freedom for a broad range of semisubmersible configurations and wave parameters. The basic elements in the theoretical model are outlined, with a more detailed discussion of the principles and derivations used to obtain the model principles and derivations used to obtain the model presented in the Appendix. presented in the Appendix. SEMISUBMERSIBLE DESCRIPTION AND EQUATIONS OF MOTION The semisubmersible is characterized as a space-frame of cylindrical members and is described geometrically by specifying end-coordinates and diameters for all of the members. Specification of the mass, moments of inertia, center of gravity and floating position are required to complete the description. The six equations of motion for the semisubmersible derive from Newton's second law for a rigid body. These differential equations, when written in matrix form, equate the product of the six-component acceleration vector, {x}, and the inertia matrix, I, to a six-component, force-moment vector, {FT}. SPEJ P. 311

Kinematic model to control the end-effector of a continuum robot for multi-axis processing

Robotica ◽  
2015 ◽  
Vol 35 (1) ◽  
pp. 224-240 ◽  
Author(s):  
Salvador Cobos-Guzman ◽  
David Palmer ◽  
Dragos Axinte
Keyword(s):  
Degrees Of Freedom ◽  
Kinematic Model ◽  
Euler Angle ◽  
Inverse Kinematic ◽  
End Effector ◽  
Six Degrees Of Freedom ◽  
Hazardous Environments ◽  
Continuum Robot ◽  
Novel Method ◽  
Six Dof

SUMMARYThis paper presents a novel kinematic approach for controlling the end-effector of a continuum robot for in-situ repair/inspection in restricted and hazardous environments. Forward and inverse kinematic (IK) models have been developed to control the last segment of the continuum robot for performing multi-axis processing tasks using the last six Degrees of Freedom (DoF). The forward kinematics (FK) is proposed using a combination of Euler angle representation and homogeneous matrices. Due to the redundancy of the system, different constraints are proposed to solve the IK for different cases; therefore, the IK model is solved for bending and direction angles between (−π/2 to +π/2) radians. In addition, a novel method to calculate the Jacobian matrix is proposed for this type of hyper-redundant kinematics. The error between the results calculated using the proposed Jacobian algorithm and using the partial derivative equations of the FK map (with respect to linear and angular velocity) is evaluated. The error between the two models is found to be insignificant, thus, the Jacobian is validated as a method of calculating the IK for six DoF.

Marine Vessel Dynamics Using 6-DOF Simulations

2008 ◽  
Author(s):  
Craig J. Pregnalato ◽  
Kyong-Huhn Lee
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
High Amplitude ◽  
Cfd Simulations ◽  
Six Degrees Of Freedom ◽  
Interface Capturing ◽  
Surface Ship ◽  
Vessel Motion ◽  
Marine Vessels ◽  
Fully Coupled

The response of marine vessels to steady currents and unsteady wave motions is presented using six degrees-of-freedom CFD simulations. The equations governing the fluid flow are coupled with the rigid-body equations of motion to predict the response of surface ships when driven by high-amplitude waves. In addition, the maneuvering performance of a submarine is analysed for a constant heading and depth. Such fully coupled simulations allow the accurate prediction of the hydrodynamic forces acting on the vessel as well as the corresponding vessel motion and are becoming increasingly important from a design standpoint. In these simulations, a high-resolution interface-capturing scheme is used to efficiently capture the dynamics of breaking and overturning waves and to examine their impact on a surface ship. The dynamics of the vessel are investigated in detail with particular emphasis on its angular response (i.e. pitch, roll and yaw).

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