運(yùn)動(dòng)中的拋射物數(shù)學(xué)(英文)
定 價(jià):38 元
- 作者:[澳] 內(nèi)維爾·德·梅斯特雷(Neville,de,Mestre) 著
- 出版時(shí)間:2020/10/1
- ISBN:9787560391571
- 出 版 社:哈爾濱工業(yè)大學(xué)出版社
- 中圖法分類:O315
- 頁(yè)碼:189
- 紙張:膠版紙
- 版次:1
- 開(kāi)本:16開(kāi)
《運(yùn)動(dòng)中的拋射物數(shù)學(xué)(英文)》共八章,前七章介紹了彈丸運(yùn)動(dòng)中所需要的數(shù)學(xué)原理,并用數(shù)學(xué)知識(shí)解決了彈丸運(yùn)動(dòng)中遇到的問(wèn)題。第八章對(duì)體育和娛樂(lè)中涉及的數(shù)學(xué)知識(shí)進(jìn)行了調(diào)查,通過(guò)各種游戲中球的運(yùn)動(dòng)、飛盤運(yùn)動(dòng)、滑雪跳躍運(yùn)動(dòng)等詳細(xì)討論了所涉及的數(shù)學(xué)理論,最后還給出這些問(wèn)題的研究現(xiàn)狀!哆\(yùn)動(dòng)中的拋射物數(shù)學(xué)(英文)》還從粒子在恒定重力下的運(yùn)動(dòng)入手,討論了許多修正(如阻力、科里奧利力、空氣動(dòng)力、自旋效應(yīng))的結(jié)果。該書(shū)的前幾章可以很好地為本科生提供有趣問(wèn)題的來(lái)源,后面的章節(jié)和參考文獻(xiàn)可以為研究生或教師提供相關(guān)的研究資料。
A large number of sporting events contain the motion of a projectile; yet research papers have appeared only intermittently on the mathematical techniques '.associated with projectiles in sport. A recent book by Hart and Croft (1988) presents a subset of these techniques for a small selection of events. The aim of the current book is to present a unified collection of the many problems that can be tackled and of all the mathematical techniques that can be employed.
The mathematical foundations of the subject of projectiles were deve-oped from investigations of the motion of bullets and shells. There are some excellent
texts describing this research in detail, the best being by McShane, Kelley and Reno (1953). Emphasis here will be on the non-military applications of the behaviour of projectiles in flight, which have received only limited attention.
The purpose of the book is to collect together the various mathematical tools and techniques that will help the reader solve many projectile problems associated with sport or recreation. It begins at an undergraduate level, and emphasises the usefulness of this special topic as a way of teaching mathematical modelling (de Mestre,1977). A basic knowledge of classical dynamics, calculus, vectors, differential equations and their numerical solution is assumed. At the end of each chapter are exercises,many of which lead on to suitable research projects for honours or masters students.
More substantial research topics are indicated in the last chapter, which surveys the application of the mathematical tools and techniques to many recreational and sporting projectile problems.
The first seven chapters of the book encompass material that has been presented to mathematics students at the R.oyal Military College, Duntroon (1972-1985) and the Australian Defence Force Academy (1986-1988). It analyses the mathe-matical solution of the equations governing the motion of a projectile during its flight through the air, this motion being generally controlled by gravitational and aero-dynamical forces. Although the physical aspects of projectile flight are important,ranging from internal ballistics of a gun, stability, in-flight measurements, through to impact on the ground, they have not been considered in great detail since this has been admirably investigated for military projectiles by Farrar and Leeming (1983), and for other projectiles in some of the many references listed at the end.
PREFACE
1.MOTION UNDER GRAVITY ALONE
1.1 Gravity
1.2 Velocity and Position Vectors
1.3 Point of Impact
1.4 The Vertex of the Trajectory
1.5 Projection from a Different Level
1.6 Inclined Plane
1.7 Enveloping Parabola
1.8 Dimensionless Equations
1.9 Exercises
2.MOTION IN A LINEAR RESISTING MEDIUM
2.1 Velocity and Position Vectors
2.2 Maximum Height
2.3 Impact Time to the Horizontal Plane
2.4 Range on the Horizontal Plane
2.5 Envelopes
2.6 Inclined Planes
2.7 Curve of Safety
2.8 Exercises
3.MOTION IN A NON-LINEAR RESISTING MEDIUM
3.1 Non-linear Drag
3.2 Cartesian Equations for Power-law Drag
3.3 Acceleration Components
3.4 Power-law Solution
3.5 Applications of the Power-law Solution
3.6 Other Non-linear Drag Functions
3.7 Exercises
4.THE BASIC EQUATIONS AND THEIR NUMERICAL SOLUTION
4.1 The Basic Equations
4.2 Ballistic Table Computations
4.3 Simple Application
4.4 Range Tables
4.5 Variations within the Basic Equations
4.6 Graphical Technique
4.7 Exercises
5.SMALL DRAG OR SMALL GRAVITY
5.1 Perturbation Techniques
5.2 Gravity or Drag Perturbations
5.3 Exercises
6.CORRECTIONS DUE TO OTHER EFFECTS
6.1 Effects Other Than Constant Gravity and Variable Drag
6.2 Coriolis Corrections
6.3 Gravity Corrections
6.4 Density, Temperature, Pressure and Humidity Variations
6.5 Lift and Sideways Aerodynamic Corrections
6.6 Wind Corrections
6.7 Overturning Moment
6.8 Differential Corrections
6.9 Exercises
7.SPIN EFFECTS
7.1 Overcoming Yaw
7.2 Spin Stabilisation of Shells
7.3 Spinning Spheres
7.4 Fluid Dynamics
7.5 The Magnus Effect
7.6 The Swing of a Cricket Ball
7.7 Spinning Seeds
7.8 The Equations of Motion for a Spinning Shell
7.9 Exercises
8.PROJECTILES IN SPORT AND RECREATION
8.1 Classes of Projectiles
8.2 Drag-to-weight Ratio
8.3 Shot-put and Hammer Throw
8.4 Basketball
8.5 Tennis, Table Tennis and Squash
8.6 Badminton
8.7 Golf
8.8 Cricket
8.9 Baseball
8.10 Soccer
8.11 Rugby and Australian Rules Football
8.12 Javelin
8.13 Discus, Frisbee and Flying Ring
8.14 Long Jump, High Jump and Ski Jump
8.15 Boomerangs
8.16 Water Jets
8.17 Cars and Cycles
8.18 Seed Dispersal
8.19 The Longest Throw or Kick
8.20 Exercises
REFERENCES
INDEX
編輯手記