structured_dictionary:general

Under this heading is listed a number of general terms frequently encountered in the field of naval architecture and marine engineering. To ensure that their general meanings are retained and that they are employed in the proper manner, their definitions are given here.

Generally a system of rectangular Cartesian co-ordinates and in particular:

**Body axes**(*x*,*y*,*z*)

A right hand orthogonal system fixed in the body or ship. The*x*axis is forward and parallel to the reference or baseline used to define the body’s shape. In general the x axis is directed forward, y axis to port and z axis upward.**NOTE This definition deviates from the ISO Definition**. For dynamic considerations the origin should be at the centre of the gravity of the body and the*z*axis vertically downwards. The*y*axis is to starboard.**Fixed axes**(*x*,_{0}*y*,_{0}*z*)_{0}

A right hand system nominally fixed in relation to the earth; the positive*z*axis is vertically downwards and the_{0}*x*axis lies in the direction of initial motion._{0}

Requires evaluating expectations of functions of random quantities as a basis for inference, where these quantities may have posterior distributions which are multivariate or of complex form or often both. This meant that for many years Bayesian statistics was essentially restricted to conjugate analysis, where the mathematical form of the prior and likelihood are jointly chosen to ensure that the posterior may be evaluated with ease. Numerical integration methods based on analytic approximations or quadrature were developed in 70's and 80's with some success,but a revolutionary change occurred in the early 1990s with the adoption of indirect methods, notably Markov Chain Monte Carlo (MCMC).

(Wikipedia) is one of the most popular interpretations of the concept of probability. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with uncertain statements. To evaluate the probability of a hypothesis, the Bayesian probabilist specifies some prior probability, which is then updated in the light of new relevant data. The Bayesian interpretation provides a standard set of procedures and formulae to perform this calculation

Adjusts probabilities given new evidence in the following way:

<m>P(H|D) = {P(D|H)P(H)}/{P(D)}</m>

where

*H*is a hypothesis, and*D*is the data.*P(H)*is the*prior probability of H:*the probability that*H*is correct before the data*D*was seen.*P(D | H)*is the conditional probability of seeing the data*D*given that the hypothesis*H*is true.*/P(D | H)*is called the*likelihood.**P(D)*is the marginal probability of*D.**P(H | D)*is the*posterior probability:*the probability that the hypothesis is true, given the data and the previous state of belief about the hypothesis.*P(D)*is the prior probability of witnessing the data*D*under all possible hypotheses. Given any exhaustive set of mutually exclusive hypotheses*Hi*, we have:

<m>P(D) = sum{i}{}{}P(D,H_i)=sum{i}{}{}P(D|H_i)P(H_i)</m>

We can consider i here to index alternative worlds, of which there is exactly one which we inhabit,
and *Hi* is the hypothesis that we are in the world *i*. *P(D, Hi)* is then the probability that we are in the world *i* and witness the data. Since the set of alternative worlds was assumed to be mutually exclusive and exhaustive, the above formula is a case of the law of alternatives.
*P(D)* is the normalizing constant, which in many cases need not be evaluated. As a result, Bayes'
formula is often simplified to:

<m>P(H|D)alphaP(D|H) P(H)</m>

where <m>alpha</m> denotes proportionality.

In general, Bayesian methods are characterized by the following concepts and procedures:

- The use of hierarchical models, and the marginalization over the values of nuisance parameters. In most cases, the computation is intractable, but good approximations can be obtained using Markov chain Monte Carlo methods.
- The
*sequential use of the Bayes' formula:*when more data becomes available after calculating a posterior distribution, the posterior becomes the next prior. Example: analysis of space launch failure rate as launches progress including analyzing near misses. - In frequentist statistics, a hypothesis is a proposition (which must be either true or false), so that the (frequentist) probability of a frequentist hypothesis is either one or zero. In Bayesian statistics, a probability
*H*represents a specific hypothesis, which may or may not be some null hypothesis.

is that property of a solution to a differential equation to remained bounded that is remain within a
certain prescribed non-infinite value or not diverge beyond a certain value.

**Safe Basin** — that region in the phase space or Poincare map where solutions remain bounded

As a noun, is applied to the act of controlling or directing, such as when controlling the movements of body or directing a ship in the steering, turning, and diving manoeuvres.

The rudders, hydroplanes, and other hinged or movable device used for controlling the motions of body or ship.

That quality of a body or ship which determines the effectiveness of movement of the controls in the producing any desired change, at a specified rate in the attitude or position of the moving body or ship.

The means or system provided to enable the crew of a ship to control its speed, power, attitude, direction of motion, and the like.

As an adjective, pertains to motion as the result of force, or to bodies and system in motions; in this respect it is opposite of *static* (which see)

That property of body which cause it, when slightly disturbed from a steady motion, to resume that the same steady motion, usually along a different path, without any corrective control being applied.

A state of balance, between opposing forces or actions.

As an adjective, often applies in English-speaking countries to the ratio between some quantity to be defined and a standard quantity having the same characteristics, which is take as a reference. The best known term of this kind is the expression “specific gravity”. Here the specific gravity is the dimensionless ratio of weight of unit volume of the designated substance to the weight of unit volume of fresh water. In other countries the term “specific” generally refer to absolute values per unit volume and is not expressed in terms of properties of a reference substance, such as water.

The property, quality, or characteristic of a body, which cause it, when its equilibrium is disturbed, to develop forces or moments acting to restore its original condition.

As an adjective, pertains to bodies or system at rest or forces in equilibrium; in this respect it is the opposite of *dynamic* (which see).

This applies to a condition may be static, but is generally dynamic, in which there is no change with time. A ship moving in a straight line at uniform speed and a ship in a steady turn at uniform speed both represent steady state conditions.

These apply to a condition which is invariably dynamic, in which the motion of body or the flow of a liquid changes with time, with reference to an assumed set of axes.

Under this heading definitions or descriptions are given of a number of liquid properties and physical constants concerned of ship hydrodynamics.

A form of surface tension, by which a molecular force exist between the surface of a liquid and a solid. The surface of the liquid may thereby be elevated or depressed.

(*σ*) [M T^{-2}]

Surface tension per unit length.

( - ) [LM^{-1} T^{2}]

The reciprocal of the volume or bulk modulus of elasticity. (See: *Modulus of elasticity, volume or bulk*)

(*ρ*) [L^{-3}] M]

The mass per unit volume of a substance. ^{1)}

(*w*) [L^{-2} M T^{-2}]

The weight per unit volume of a substance.

(*g*) [L T^{-2}]

The acceleration, due to earth’s gravity field, of a freely falling body in a vacuum. This is not strictly constant and over the earth’s surface it varies by as much as ½%. For most terrestrial engineering purposes it is usual to disregard this variation and for convenience the following international standard value has been agreed: 9.80665 m/s2 (32.1737 ft/s2).

(*E*) [L^{-1} M T^{-2}]

The ratio of the stress, or force per unit area, to the corresponding change of volume per unit volume.

(*γ*) [-]

The ratio of density of any substance to the density of fresh water at 4° Centigrade. In English speaking countries the concept expressed is called Specific gravity.

The relative capability of being dissolved

[L^{3} M^{-1}]

The volume of a substance per unit mass; the reciprocal of mass density (See: Density , mass)

(-) [-]

See: *Relative mass or weight*.

The property of the interface between two immiscible fluids of behaving as if it were a film under tension.

The pressure of vapour in equilibrium with its liquid state. It is also called the saturated vapour pressure or vapour tension, which for a given substance depends only upon the temperature.

(*μ*) [L^{-1} M T^{-1}] ^{2)}

The ratio of the shearing stress in a fluid to its rate of shear deformation. See also: *Resistance section*.

(*ν*) [L^{2} T^{-1}] ^{3)}

The ratio of the coefficient of dynamic viscosity to the mass density of a fluid. See also: *Resistance section*.

^{4)}

*

* For standard values of fresh water and salt water at 15° C (59° F) see: *Performance Section* under “Water standard fresh and salt”. For values over a range of temperature in S.I units see in “Metrication Ship Research and Design”, Paffett, J.A.H. Trans. RINA, 1971; for corresponding values in Imperial Unit see Proceedings 10th International Towing Tank Conference, London 1963 or National Physical Laboratory, Ship Division Report No. 81 (1966).

structured_dictionary/general.txt · Last modified: 2016/04/11 17:18 by ubuwiki

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