Branches of Mechanics

There are three branches of mechanics. Classical mechanics normally deals with things in the everyday world accelerating sports cars, bodies sliding down inclined planes and other related phenomena. 

Relativistic mechanics normally deals with situations where one body is moving with respect to another one. If this relative motion is one of uniform velocity, then the subject is referred to as special relativity. Special relativity is well understood and has stood the test of experiment. If accelerations are involved, then we enter the realm of general relativity. It is fair comment to say that general relativity is still an active research field. 

Finally we have quantum mechanics, which normally has to be invoked when dealing with situations where small particles (such as electrons, protons and neutrons) are involved. 

In the following sections, I have tried to pick out some of the more familiar techniques and concepts that will form recurring themes throughout the text. 

I assume that you are familiar with the elementary ideas of vectors and vector algebra. Thus if a point P has position vector r (I will use bold letters to denote vectors) then we can write r in terms of the unit Cartesian vectors ex, ey and ez as  

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The branch of science related to the study of deformation and flow of materials was given the name rheology by Bingham, whom some call the father of modern rheology. The prefix rheo is derived from the Greek rheos, meaning current of flow. The study of rheology includes two vastly different branches of mechanics—fluid and solid. The polymer scientist is usually concerned with viscoelastic materials that act as both solids and liquids. 

Difficulties of this kind have deterred the author from attempting to explain the mysteries of nature, and have forced him to the more modest aim of deducing some of the more obvious propositions relating to the statistical branch of mechanics. Here, there can be no mistake in regard to the agreement of the hypotheses with the facts of nature, for nothing is assumed in that respect. The only error into which one can fall, is the want of agreement between the premises and the conclusions, and this, with care, one may hope, in the main, to avoid. 

The foregoing account dealt chiefly with the conceptual foundations of statistico-mechanical investigations. Accordingly we had to emphasize that in these investigations a large number of loosely formulated and perhaps even inconsistent statements occupy a central position. In fact, we encounter here an incompleteness which from the logical point of view is serious and which appears in other branches of mechanics to a much smaller extent. This incompleteness, however, does not seem to have influenced the physicists in their evaluation of the... 

A branch of mechanics dealing with the motion of rigid bodies without reference to their masses or the forces acting on the bodies, kite... 

Computational fluid dynamics involves the analysis of fluid flow and related phenomena such as heat and/or mass transfer, mixing, and chemical reaction using numerical solution methods. Usually the domain of interest is divided into a large number of control volumes (or computational cells or elements) which have a relatively small size in comparison with the macroscopic volume of the domain of interest. For each control volume a discrete representation of the relevant conservation equations is made after which an iterative solution procedure is invoked to obtain the solution of the nonlinear equations. Due to the advent of high-speed digital computers and the availability of powerful numerical algorithms the CFD approach has become feasible. CFD can be seen as a hybrid branch of mechanics and mathematics. CFD is based on the conservation laws for mass, momentum, and (thermal) energy, which can be expressed as follows ... 

While fitting parameters of a small system of odes to experimental data lies in the realm of empirical modelling, fitting parameters in a similar way to results of calculations from a detailed kinetic model can be considered as a branch of mechanism reduction. 

The subject of statistical mechanics is a branch of mechanics which has been found very useful in the discussion of the properties of complicated systems, such as a gas. In the following sections we shall give a brief discussion of the fundamental theorem of statistical quantum mechanics (Sec. 49a), its application to a simple system (Sec. 496), the Boltzmann distribution law (Sec. 49c), Fermi-Dirac and Bose-Einstein statistics (Sec. 49d), the rotational and vibrational energy of molecules (Sec. 49e), and the dielectric constant of a diatomic dipole gas (Sec. 49/). The discussion in these sections is mainly descriptive and elementary we have made no effort to carry through the difficult derivations or to enter into the refined arguments needed in a... 

Branch of mechanics where the properties of individual constituents such as matrix and fiber are used to estimate the structural... 

Soil Mechanics. Most people would not consider soil as an engineering material, but it is, because most constructed structures are situated on it by necessity. Without due consideration of soils bearing capacity under various circumstances, a structure built over it may sink, tilt, or outright turn over. Soil mechanics is a branch of mechanics that studies the mechanical properties of various types of soil and its strength at different moisture-content levels. It provides the scientific base upon which design formulas and codes are developed for everyday engineering design practice. 

Rotational mechanics is a branch of mechanics that is identified with a special energy variety bearing the same name. It includes two energy subvarieties inductive and capacitive. 

Dynamics Branch of mechanics that studies systems that are in motion, subject to acceleration or deceleration. 

Hydraulic engineering is often mistakenly thought to be petroleum engineering, which deals with the flow of natural gas and oil in pipelines, or the branch of mechanical engineering that deals with a vehicle s engine, gas pump, and hydraulic breaking system. The only machines that are of concern to hydraulic engineers are hydraulic turbines and water pumps. 

A mechanical system may consist of several different parts. When such a part is able to undergo deformations, it will be regarded as a deformable structure. It may be modeled with a certain complexity, for example with the aid of shell or beam theory, but can be traced back to the basic configuration of the continuum, which is the subject of investigation within the homonymous branch of mechanics. Such a continuum is a continuous domain of spatial,... 

Kinematics is the branch of mechanics that explores the motion of material bodies from the standpoint of their space-time relationships, disregarding their masses and the forces acting on them. 

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