تکنولوژیمهندسی مکانیک

فرمت: pdf
حجم: 2.9 مگابایت
قیمت: 2000 تومان

Galilean Mechanics and Thermodynamics of Continua

By


شناسنامه فارسی کتاب:
عنوان کتاب:

مکانیک گالیله و ترمودینامیک با زنجیره

موضوع کتاب:

Technology, Mechanical Engineering

سال نشر:
ناشر: Wiley
ویرایش:
شماره جلد:
تعداد صفحه: 450
زبان: انگلیسی
This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of the classical tensors, this approach allows gathering the usual mechanical entities - mass, energy, force, moment, stresses, linear and angular momentum - in a single tensor.

Starting with the basic subjects, and continuing through to the most advanced topics, the authors' presentation is progressive, inductive and bottom-up. They begin with the concept of an affine tensor, a natural extension of the classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics - torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi
Part 1. Particles and Rigid Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 1. Galileo’s Principle of Relativity . . . . . . . . . . . . . . . . . . . . .3
1.1. Events and space–time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2. Event coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.1. When? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2. Where? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3. Galilean transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1. Uniform straight motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2. Principle of relativity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.3. Space–time structure and velocity addition . . . . . . . . . . . . . . . . . . 10
1.3.4. Organizing the calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.5. About the units of measurement . . . . . . . . . . . . . . . . . . . . . . . . 12
1.4. Comments for experts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Chapter 2. Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2. Statical torsor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.1. Two-dimensional model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.2. Three-dimensional model . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2.3. Statical torsor and transport law of the moment . . . . . . . . . . . . . . . 18
2.3. Statics equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1. Resultant torsor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.2. Free body diagram and balance equation . . . . . . . . . . . . . . . . . . . . 20
2.3.3. External and internal forces . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4. Comments for experts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 3. Dynamics of Particles . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1. Dynamical torsor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.1.1. Transformation law and invariants . . . . . . . . . . . . . . . . . . . . . . 27
3.1.2. Boost method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.2. Rigid body motions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.1. Rotations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2.2. Ri ..
شابک/ISBN: 978-1-84821-642-6