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.

DYNAMIC SIMULATION OF A SPATIAL 3-DOF TENSEGRITY MECHANISM

2005 ◽  
Vol 29 (4) ◽  
pp. 491-505 ◽  
Author(s):  
Marc Arsenault ◽  
Clément M. Gosselin
Keyword(s):  
Dynamic Model ◽  
Dynamic Simulation ◽  
Dynamic Problem ◽  
Degrees Of Freedom ◽  
Dynamic Behaviour ◽  
Equations Of Motion ◽  
Attractive Alternative ◽  
Equilibrium Configurations ◽  
Geometrical Constraints ◽  
Three Degree Of Freedom

Tensegrity mechanisms have the advantage of being relatively lightweight due to. their extensive use of cables and springs. As such, they have the potential of being an attractive alternative to conventional mechanisms in certain application environments. However, the presence of unconstrained degrees of freedom in tensegrity mechanisms leads to a dynamic behaviour that cannot be directly controlled with the actuators. In this work, the dynamic model of a novel spatial three-degree-of-freedom (3-DOF) tensegrity mechanism is developed using the Lagrangian formulation. The resulting equations of motion are then solved to simulate the mechanism's motion between equilibrium configurations. Since the mechanism is subjected to holonomic nonlinear geometrical constraints, these must be considered during the solution of its forward dynamic problem. It is seen that the use of damping in the springs is not very efficient in dissipating the mechanism's energy during motion.

Dynamic Analysis of Flexible Gear Trains/Transmissions: An Automated Approach

1992 ◽  
Vol 59 (4) ◽  
pp. 976-982 ◽  
Author(s):  
F. M. L. Amirouche ◽  
N. H. Shareef ◽  
M. Xie
Keyword(s):  
Dynamic Analysis ◽  
Strain Energy ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Elastic Behavior ◽  
Flexible Bodies ◽  
Gear Teeth ◽  
Six Degrees Of Freedom ◽  
Gear Trains

In this paper an automated algorithmic method is presented for the dynamic analysis of geared trains/transmissions. These are treated as a system of interconnected flexible bodies. The procedure developed explains the switching of constraints with time as a result of the change in the contacting areas at the gear teeth. The elastic behavior of the system is studied through the employment of three-dimensional isoparametric elements having six degrees-of-freedom at each node. The contact between the bodies is assumed at the various nodes, which could be either a line or a plane. The kinematical expressions, together with the equations of motion using Kane’s method, strain energy concepts, are presented in a matrix form suitable for computer implementation. The constraint Jacobian matrices are generated automatically based on the contact information between the bodies. The concepts of the relative velocity at the contacting points at the tooth pairs and the subsequent use of the transmission ratios in the analysis is presented.

Investigation of Train Dynamics in Passing Through Curves Using a Full Model

Joint Rail ◽  
2004 ◽  
Author(s):  
Mohammad Durali ◽  
Mohammad Mehdi Jalili Bahabadi
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Full Model ◽  
Bogie Frame ◽  
Nonlinear Characteristics ◽  
Train Derailment ◽  
Train Dynamics

In this article a train model is developed for studying train derailment in passing through bends. The model is three dimensional, nonlinear, and considers 43 degrees of freedom for each wagon. All nonlinear characteristics of suspension elements as well as flexibilities of wagon body and bogie frame, and the effect of coupler forces are included in the model. The equations of motion for the train are solved numerically for different train conditions. A neural network was constructed as an element in solution loop for determination of wheel-rail contact geometry. Derailment factor was calculated for each case. The results are presented and show the major role of coupler forces on possible train derailment.

Trajectory Tracking of Underactuated Multibody Systems

2011 ◽  
Author(s):  
Stefan Reichl ◽  
Wolfgang Steiner
Keyword(s):  
Trajectory Tracking ◽  
Multibody Systems ◽  
Degrees Of Freedom ◽  
Inverse Dynamics ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
State Variables ◽  
Algebraic Equations

This work presents three different approaches in inverse dynamics for the solution of trajectory tracking problems in underactuated multibody systems. Such systems are characterized by less control inputs than degrees of freedom. The first approach uses an extension of the equations of motion by geometric and control constraints. This results in index-five differential-algebraic equations. A projection method is used to reduce the systems index and the resulting equations are solved numerically. The second method is a flatness-based feedforward control design. Input and state variables can be parameterized by the flat outputs and their time derivatives up to a certain order. The third approach uses an optimal control algorithm which is based on the minimization of a cost functional including system outputs and desired trajectory. It has to be distinguished between direct and indirect methods. These specific methods are applied to an underactuated planar crane and a three-dimensional rotary crane.

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.

Toward a Minimal Dynamic Model of a 6-DOF Parallel Robot

1997 ◽  
Author(s):  
L. Beji ◽  
M. Pascal ◽  
P. Joli
Keyword(s):  
Dynamic Model ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Parallel Robot ◽  
Form Solution ◽  
Lagrangian Formalism ◽  
Inverse Kinematic Problem ◽  
Geometrical Properties

Abstract In this paper, an architecture of a six degrees of freedom (dof) parallel robot and three limbs is described. The robot is called Space Manipulator (SM). In a first step, the inverse kinematic problem for the robot is solved in closed form solution. Further, we need to inverse only a 3 × 3 passive jacobian matrix to solve the direct kinematic problem. In a second step, the dynamic equations are derived by using the Lagrangian formalism where the coordinates are the passive and active joint coordinates. Based on geometrical properties of the robot, the equations of motion are derived in terms of only 9 coordinates related by 3 kinematic constraints. The computational cost of the obtained dynamic model is reduced by using a minimum set of base inertial parameters.

On the Radiation and Diffraction of Surface Waves by Submerged Spheroids

1989 ◽  
Vol 33 (02) ◽  
pp. 84-92
Author(s):  
G. X. Wu ◽  
R. Eatock Taylor
Keyword(s):  
Degrees Of Freedom ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Added Mass ◽  
Wave Radiation ◽  
Legendre Functions ◽  
Incoming Wave ◽  
Six Degrees Of Freedom ◽  
Damping Coefficients ◽  
Exciting Forces

The problem of wave radiation and diffraction by submerged spheroids is analyzed using linearized three-dimensional potential-flow theory. The solution is obtained by expanding the velocity potential into a series of Legendre functions in a spheroidal coordinate system. Tabulated and graphical results are provided for added mass and damping coefficients of various spheroids undergoing motions in six degrees of freedom. Graphs are also provided for exciting forces and moments corresponding to a range of incoming wave angles.

Development of a Numerical Method for the Calculation of Power Absorption by Arrays of Similar Arbitrarily Shaped Bodies in a Seaway

1982 ◽  
Vol 26 (01) ◽  
pp. 38-44
Author(s):  
James H. Duncan ◽  
Clinton E. Brown
Keyword(s):  
Wave Energy ◽  
Degrees Of Freedom ◽  
Linear Array ◽  
Three Dimensional ◽  
Computational Procedure ◽  
Hydrodynamic Theory ◽  
Optimal Solutions ◽  
Power Absorption ◽  
Six Degrees Of Freedom ◽  
First Order

A computational procedure is developed using first-order hydrodynamic theory to predict the motions and power absorption from arrays of similar three-dimensional buoys. The buoy shape and the number and placement of the buoys may be arbitrarily selected. The program provides for waves of selected frequency and direction or combinations thereof by simple superposition; thus, the effects on energy absorption of wave energy spectral distributions or short-crestedness can be analyzed. The computer model has been validated by comparison of its results with published analytically derived power optimal solutions for five buoys in a linear array. The program provides the power output of each buoy in the array with the associated motions in six degrees of freedom. The limited number of cases studied has provided the interesting result that identical buoys in an array tend to absorb wave energy at rates close to those of optimized systems for which buoy amplitude and phasing would have to be controlled.

scholarly journals Effective 1D Time-Dependent Schrödinger Equations for 3D Geometrically Correlated Systems

Materials ◽  
2020 ◽  
Vol 13 (13) ◽  
pp. 3033
Author(s):  
Devashish Pandey ◽  
Xavier Oriols ◽  
Guillermo Albareda
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Time Dependent ◽  
Ab Initio Molecular Dynamics ◽  
Quantitative Accuracy ◽  
Dimensional Simulation ◽  
Transport Problems ◽  
Computational Resources

The so-called Born–Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows effectively separating fast and slow degrees of freedom and thus treating electrons and nuclei with different mathematical footings. Here, we consider the use of a Born–Huang-like expansion of the three-dimensional time-dependent Schrödinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a typical two-dimensional geometrical constriction and upto three orders for three-dimensional constriction.

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.

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