Introduction .................................................. VII
Part I
1. h - Geometry. Neo-Sines: Functions
with Altitude as an Argument ............................... 13
2. Triangle ................................................... 37
3. Ellipse .................................................... 43
Part II
4. Application of h-Geometry in Mathematics
and Engineering Science .................................... 49
4.1. Mathematical Model to Calculate Coordinates
of Earth Satellites .................................. 49
4.1.1. Two-dimensional model ........................ 50
4.1.2. Three-dimensional model ...................... 54
4.2. h-Geometry in Finite Element Computation ............. 60
4.2.1. Mathematical Model of Finite Element Based
on h-Geometry ................................ 62
4.2.2. Mathematical Model of a Two-Element System ... 67
4.3. Theoretical Mechanics - Statics ...................... 75
4.4. Theory of Mechanisms - Kinematics .................... 81
4.5. Aerodynamics and Hydrodynamics - Basic
Characteristics ...................................... 84
4.6. Mathematical Models for Artillery Projectile
Ballistics Based on h-Geometry ....................... 87
4.7. Operations with Vectors in h-Geometry ................ 94
4.7.1. Composition of Two Vectors ................... 94
4.7.2. Subtraction of vectors ....................... 97
4.8. Linearization in Physical Process Modelling ......... 100
Part III
5. Astronomical Calculations Based on h-Geometry ............... 99
Part IV. ANNEX. Classical Approach
A1. Classical Geometry and Trigonometry. Sine:
Functions where Arguments are Angles Measured
as the Length of the Arc of Circle ....................... 115
А2. Triangle ................................................. 119
A3. Ellipse .................................................. 127
A4. Classical Geometry and Trigonometry in Mathematics
and Technical Science .................................... 133
A4.1. Basic Methods of Determining Earth
Satellite Coordinates ............................. 133
A4.1.1. Transformation of Coordinates in
the Plane ................................ 133
A4.1.2. Transformation of Coordinates in
Three-Dimensional Space .................. 134
A4.2. Basics of the Method of Finite Elements ........... 138
A4.2.1. Mathematical Model of a Single Element ... 139
A4.2.2. Mathematical Model of a Two-Element
System ................................... 143
A4.3. Theoretical Mechanics - Statics ................... 146
A4.4. Theory of Mechanisms - Kinematics ................. 150
A4.5. Aerodynamics and Hydrodynamics -
Basic Characteristics ............................. 153
A4.6. Mathematical Models in Ballistics ................. 156
A5. Astronomical Calculations Based on Angle Trigonometry .... 169
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