Applications of the Ogilvie-Tuck Formulae to Ship Hydrodynamics

2010 ◽  
Author(s):  
Piotr J. Bandyk ◽  
Robert F. Beck ◽  
Xinshu Zhang
Keyword(s):  
Steady Flow ◽  
Degrees Of Freedom ◽  
Hydrodynamic Coefficients ◽  
Practical Applications ◽  
Classical Work ◽  
Strip Theory ◽  
The Mean ◽  
And Mathematics ◽  
Original Derivation ◽  
Ship Speed

The work of Ogilvie and Tuck [1] was critical in extending strip theory to problems with forward speed. Salvesen et al. [2] used some of those findings in their classical work to determine the hydrodynamic coefficients in five degrees-of-freedom. Other methods have also utilized the formulae with success. The original derivation makes several assumptions about the hull shape and the steady flow around it. In practice, these assumptions do not hold exactly. Other simplifications are usually made, i.e. the mean ship speed is used instead of the actual steady flow around the hull. These may violate the original assumptions, but the results are generally satisfactory. The truly elegant aspect of the Ogilvie-Tuck hydrodynamic coefficients is that they can be calculated from zero-speed results. This is a product of the approach, assumptions, and mathematics done in Appendix A of the original work [1] to derive the Ogilvie-Tuck theorem, also called Tuck’s theorem by many authors. The Ogilvie-Tuck formulae include the hydrodynamic coefficients, expressions of the mj terms, and the Ogilvie-Tuck theorem. This paper discusses the original derivation and several practical applications, including those where the assumptions may be violated. Several qualitative or quantitative statements can be made about the errors introduced by simplifications. Some computational results are presented to emphasize the significance in practical use.

The motion of a lunar orbiter

1966 ◽  
Vol 25 ◽  
pp. 373
Author(s):  
Y. Kozai
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Artificial Satellite ◽  
Equations Of Motion ◽  
Triaxial Ellipsoid ◽  
The Moon ◽  
Secular Motion ◽  
The Earth ◽  
Close Satellite ◽  
The Mean

The motion of an artificial satellite around the Moon is much more complicated than that around the Earth, since the shape of the Moon is a triaxial ellipsoid and the effect of the Earth on the motion is very important even for a very close satellite.The differential equations of motion of the satellite are written in canonical form of three degrees of freedom with time depending Hamiltonian. By eliminating short-periodic terms depending on the mean longitude of the satellite and by assuming that the Earth is moving on the lunar equator, however, the equations are reduced to those of two degrees of freedom with an energy integral.Since the mean motion of the Earth around the Moon is more rapid than the secular motion of the argument of pericentre of the satellite by a factor of one order, the terms depending on the longitude of the Earth can be eliminated, and the degree of freedom is reduced to one.Then the motion can be discussed by drawing equi-energy curves in two-dimensional space. According to these figures satellites with high inclination have large possibilities of falling down to the lunar surface even if the initial eccentricities are very small.The principal properties of the motion are not changed even if plausible values ofJ3andJ4of the Moon are included.This paper has been published in Publ. astr. Soc.Japan15, 301, 1963.

Optimal stationary strategies in leavable Markov decision processes

1990 ◽  
Vol 27 (01) ◽  
pp. 134-145
Author(s):  
Matthias Fassbender
Keyword(s):  
Transition Probabilities ◽  
Practical Applications ◽  
Stationary Strategies ◽  
Countable State ◽  
Markov Decision ◽  
Bias Optimality ◽  
The Mean ◽  
Optimal Stationary Strategies ◽  
The Cost ◽  
Reward Criterion

This paper establishes the existence of an optimal stationary strategy in a leavable Markov decision process with countable state space and undiscounted total reward criterion. Besides assumptions of boundedness and continuity, an assumption is imposed on the model which demands the continuity of the mean recurrence times on a subset of the stationary strategies, the so-called ‘good strategies'. For practical applications it is important that this assumption is implied by an assumption about the cost structure and the transition probabilities. In the last part we point out that our results in general cannot be deduced from related works on bias-optimality by Dekker and Hordijk, Wijngaard or Mann.

Maximum Total Point Motion of Five Points Versus All Points in Assessing Tibial Baseplate Stability

2021 ◽  
Author(s):  
Abigail Niesen ◽  
Anna L Garverick ◽  
Maury Hull
Keyword(s):  
Degrees Of Freedom ◽  
Stability Limit ◽  
3D Models ◽  
Six Degrees Of Freedom ◽  
Percent Error ◽  
Model Based ◽  
Point Motion ◽  
The Mean ◽  
The Difference ◽  
Total Point

Abstract Maximum total point motion (MTPM), the point on a baseplate that migrates the most, has been used to assess the risk of tibial baseplate loosening using radiostereometric analysis (RSA). Two methods for determining MTPM for model-based RSA are to use either 5 points distributed around the perimeter of the baseplate or to use all points on the 3D model. The objectives were to quantify the mean difference in MTPM using 5 points vs. all points, compute the percent error relative to the 6-month stability limit for groups of patients, and to determine the dependency of differences in MTPM on baseplate size and shape. A dataset of 10,000 migration values was generated using the mean and standard deviation of migration in six degrees of freedom at 6 months from an RSA study. The dataset was used to simulate migration of 3D models (two baseplate shapes and two baseplate sizes) and calculate the difference in MTPM using 5 virtual points vs. all points and the percent error (i.e. difference in MTPM/stability limit) relative to the 6-month stability limit. The difference in MTPM was about 0.02 mm, or 4% percent relative to the 6-month stability limit, which is not clinically important. Furthermore, results were not affected by baseplate shape or size. Researchers can decide whether to use 5 points or all points when computing MTPM for model-based RSA. The authors recommend using 5 points to maintain consistency with marker-based RSA.

Systematic Synthesis and Applications of Novel Multi-Degree-of-Freedom Differential Systems

1992 ◽  
Author(s):  
Sridhar Kota ◽  
Srinivas Bidare
Keyword(s):  
Degrees Of Freedom ◽  
Building Blocks ◽  
Degree Of Freedom ◽  
Differential Systems ◽  
Practical Applications ◽  
Epicyclic Gear ◽  
Differential Mechanism ◽  
Long Time ◽  
Gear Trains ◽  
Drive Systems

Abstract A two-degree-of-freedom differential system has been known for a long time and is widely used in automotive drive systems. Although higher degree-of-freedom differential systems have been developed in the past based on the well-known standard differential, the number of degrees-of-freedom has been severely restricted to 2n. Using a standard differential mechanism and simple epicyclic gear trains as differential building blocks, we have developed novel whiffletree-like differential systems that can provide n-degrees of freedom, where n is any integer greater than two. Symbolic notation for representing these novel differentials is also presented. This paper presents a systematic method of deriving multi-degree-of-freedom differential systems, a three and four output differential systems and some of their practical applications.

scholarly journals Quantifying the closeness to a set of random curves via the mean marginal likelihood

2020 ◽  
Author(s):  
Cédric Rommel ◽  
Joseph Frédéric Bonnans ◽  
Baptiste Gregorutti ◽  
Pierre Martinon
Keyword(s):  
Marginal Likelihood ◽  
Marginal Density ◽  
Random Curves ◽  
Practical Applications ◽  
Random Functions ◽  
Practical Usefulness ◽  
Class Of Estimators ◽  
The Mean ◽  
Multivariate Density ◽  
Aircraft Trajectories

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

scholarly journals Program Quality and Developmental Outcomes Related to Youth Volleyball in Ethiopia: Assessing Relationships and Variations

2021 ◽  
Vol 11 (4) ◽  
pp. 1388-1405
Author(s):  
Abdulaziz Mussema ◽  
Tefera Tadesse ◽  
Zelalem Melkamu
Keyword(s):  
Developmental Outcomes ◽  
Central Zone ◽  
Youth Sport ◽  
Program Quality ◽  
Cross Sectional Survey ◽  
Cross Sectional ◽  
Practical Applications ◽  
The Mean ◽  
Project Site

This study aims to assess program quality and developmental outcomes of a youth volleyball project in one of the regional states in Ethiopia, and further examine variations between groups across gender and project site zones. We applied a cross-sectional survey design, collecting quantitative data from youth volleyball players (n = 215) with a mean age of 16.18 years (SD = 0.69) through a self-reported questionnaire. The results indicated that young players’ perceptions did not vary significantly across gender, except for the mean score of the perceived experience variable for girls (M = 2.68, SD = 0.318) was significantly higher than the mean score of boys (M = 2.58, SD = 0.258). One-way (project site zone) analyses of variance (ANOVAs) identified that youth volleyball projects in the central zone were consistently rated higher than those in the western zone, except for the current practice rating. Moreover, correlation analysis results indicated the presence of a significant relationship, both within and between program quality and developmental outcome variables. Furthermore, the results of regression analysis indicated that the program quality variables together predicted each of the developmental outcomes, accounting for 18.9% to 31.7% of the variances. It is concluded that the quality of the youth volleyball program in Ethiopia varies considerably across the project site zones and the program quality variables significantly relate to the developmental outcomes measured with differential effects. The data from this study reveals several practical applications for Ethiopia and beyond in terms of guiding youth volleyball projects. Moreover, the findings of the study showed that youth sport and the manner in which it is structured and delivered to youth players influences the attainment of positive developmental outcomes. These results suggest that contextual differences really do have an effect on the quality of youth sport program processes and developmental outcomes.

scholarly journals Virtual laboratories as strategy for teaching improvement in Math Sciences and Engineering in Bolivia

2021 ◽  
Vol 14 (2) ◽  
pp. 187-196
Author(s):  
Francisco Javier Triveno Vargas ◽  
Hugo Siles Alvarado
Keyword(s):  
Differential Equations ◽  
Programming Languages ◽  
Stem Education ◽  
Degrees Of Freedom ◽  
Classical Problem ◽  
Interdisciplinary Approach ◽  
Theory And Practice ◽  
Relevant Today ◽  
Virtual Laboratories ◽  
And Mathematics

STEM education is a strategy based on four disciplines (science, technology, engineering and mathematics), integrated in an innovative interdisciplinary approach. Although, the concept of STEM education is more relevant today, the discussion of a teaching model with special attention in the four subjects aforementioned began in the early 2000s. Taking into account this context, the strategy presented in this paper has been disseminated in Bolivia’s main universities for the last five years. A country that has not yet managed to associate basic disciplines such as calculus, matrix algebra, and/or differential equations to solve problems of an applicative nature, that is, to establish the link between theory and practice. To establish the connection, it is necessary to deduce differential equations associated with practical problems; solve these equations with numerical methods, appeal to the simulation concept to later introduce programming languages like Python/VPython to build virtual laboratories. The classical problem addressed for this purpose is the satellite of two degrees of freedom.

scholarly journals Evaluation of the relationship between spatial abilities and anatomy learning

2020 ◽  
Vol 14 (2) ◽  
pp. 139-144
Author(s):  
Mustafa Aydın ◽  
Mehmet Tuğrul Yılmaz ◽  
Muzaffer Şeker
Keyword(s):  
Mental Rotation ◽  
Spatial Ability ◽  
Significant Contribution ◽  
Spatial Abilities ◽  
School Students ◽  
Mental Rotation Test ◽  
Practical Applications ◽  
Significant Difference ◽  
The Mean ◽  
The Relationship

Objectives: The aim of this study was to examine the relationship between the spatial abilities of medical school students and their learning in anatomy. Methods: The spatial abilities of the 120 students (74 females, 46 males) were examined using Mental Rotation Test (MRT). The relationship between the mental rotation scores and the mean scores of their practical and theoretical anatomy examinations was determined in terms of gender. Results: The study revealed that mental rotation skills of female participants were lower than males; however, there was no significant difference in their exam (theoretical and practical anatomy examinations) scores in terms of gender. The spatial ability of the students had a low level significant effect on their anatomy scores, regarding practical applications. Conclusion: The results of the study revealed a significant relationship between students’ spatial ability and their success in practical anatomy examinations. This suggests that improving spatial ability skills may have a significant contribution to practical anatomy learning and may be considered as a part of anatomy education.

scholarly journals Engineering the quantum-classical interface of solid-state qubits

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
David J Reilly
Keyword(s):  
Quantum Information ◽  
Solid State ◽  
Degrees Of Freedom ◽  
Technology Development ◽  
Fault Tolerant ◽  
Building Blocks ◽  
Experimental Physicist ◽  
And Mathematics ◽  
Classical Control ◽  
And Control

AbstractSpanning a range of hardware platforms, the building-blocks of quantum processors are today sufficiently advanced to begin work on scaling-up these systems into complex quantum machines. A key subsystem of all quantum machinery is the interface between the isolated qubits that encode quantum information and the classical control and readout technology needed to operate them. As few-qubit devices are combined to construct larger, fault-tolerant quantum systems in the near future, the quantum-classical interface will pose new challenges that increasingly require approaches from the engineering disciplines in combination with continued fundamental advances in physics, materials and mathematics. This review describes the subsystems comprising the quantum-classical interface from the viewpoint of an engineer, experimental physicist or student wanting to enter the field of solid-state quantum information technology. The fundamental signalling operations of readout and control are reviewed for a variety of qubit platforms, including spin systems, superconducting implementations and future devices based on topological degrees-of-freedom. New engineering opportunities for technology development at the boundary between qubits and their control hardware are identified, transversing electronics to cryogenics.

A Nonlinear Mathematical Model for Ship Turning Circle Simulation in Waves

2005 ◽  
Vol 49 (02) ◽  
pp. 69-79 ◽  
Author(s):  
Ming-Chung Fang ◽  
Jhih-Hong Luo ◽  
Ming-Ling Lee
Keyword(s):  
Mathematical Model ◽  
Degrees Of Freedom ◽  
Regular Waves ◽  
Nonlinear Mathematical Model ◽  
Ship Maneuvering ◽  
Sea Trial ◽  
Six Degrees Of Freedom ◽  
Strip Theory ◽  
Calm Water ◽  
Maneuvering Motion

In the paper, a simplified six degrees of freedom mathematical model encompassing calm water maneuvering and traditional seakeeping theories is developed to simulate the ship turning circle test in regular waves. A coordinate system called the horizontal body axes system is used to present equations of maneuvering motion in waves. All corresponding hydrodynamic forces and coefficients for seakeeping are time varying and calculated by strip theory. For simplification, the added mass and damping coefficients are calculated using the constant draft but vary with encounter frequency. The nonlinear mathematical model developed here is successful in simulating the turning circle of a containership in sea trial conditions and can be extended to make the further simulation for the ship maneuvering under control in waves. Manuscript received at SNAME headquarters February 19, 2003; revised manuscript received January 27, 2004.

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