Contents

• Applied Mathematics
• Numerical Methods
• Algebraic and Transcendental Equations
• Introduction
• Method of iterations
• Method of tangents
• Method of halving
• Method of chords
• Examples
• References
• Software
• Interpolation of Functions
• Introduction
• Newton’s first interpolation formula
• Newton’s second interpolation formula
• Stirling’s interpolation formula
• The spline interpolation
• Example
• References
• Software
• Numerical Differentiaon
• Introduction
• Formulas of numerical differentiaon
• Example
• References
• Software
• Numerical Integration
• Introduction
• The trapezoid rule
• Simpson’s rule
• Examples
• References
• Software
• Ordinary Differential Equations
• Introduction
• Euler’s method
• Runge-Kutta method
• Examples
• References
• Software
• Partial Differential Equations
• Introduction
• Method of finite differences / Method of grids
• Example: solution of the elliptic equation
• Method of characteristics
• Example: solution of the hyperbolic equation
• References
• Software
• Mathematical Statistics
• Elements of Mathematical Statistics
• Subject and problems of mathematical statistics
• Random variables and distribution laws
• Numerical characteristics of random variables
• Distributions of discrete random variables
• Distributions of continuous random variables
• Systems of random variables
• Examples
• References
• Software
• Treatment of Experiment Results
• Alignment of statistical distributions. Pearson’s curves
• Agreement criteria
• Regression analysis. The least squares smoothing
• Example
• References
• Software
• Matrix Algebra
• Principles of Matrix Calculation
• Introduction
• The basic definitions
• Operations with matrices
• The transposed matrix
• The inverse matrix
• Powers of matrices
• Rank of matrix
• Cellular matrices
• Triangular matrices
• Elementary transformations of matrices
• Example
• References
• Engineering Mathematics
• Mobile Machines
• Tractive Analysis
• Introduction
• One engine transmission
• Scheme and elements of one engine transmission
• System of equations
• Method of solution
• Example
• Two engines transmission
• Scheme and elements of two engines transmission
• System of equations
• Method of solution
• Example
• References
• Software DRAWN
• Hydraulic Systems
• Dynamic Analysis
• Introduction
• Structure description of hydraulic circuits
• Library of hydraulic elements and mathematical models
• Forming and solving algorithms of hydraulic circuit mathematical model
• Form of the analysis results presentation
• Examples
• References
• Software HYDRA
• Static Analysis
• Introduction
• Structure description of hydraulic circuits
• Library of hydraulic elements and mathematical models
• General scheme of solution
• Form of the analysis results presentation
• Example
• References
• Software HYSTR
• Dynamic Express Analysis
• Introduction
• Typical structures of hydraulic circuits and their description
• Library of mathematical models of functional blocks
• Forming of hydraulic circuit mathematical model and algorithm of solution
• Example: dynamics of hydraulic drive of asphalt spreader
• References
• Software HYDЕA
• Synthesis of Hydraulic Circuits
• Introduction
• Library of standard graphical symbols of hydraulic elements
• Forming of principal hydraulic circuits
• Forming of simplified hydraulic circuits
• References
• Software
• Dynamic Synthesis of Hydraulic Devices
• Dynamic synthesis of throttle braking devices of hydraulic cylinders. Introduction
• Planning of the piston braking law
• Algorithm of dynamic synthesis
• Examples of dynamic synthesis
• References
• Software
• Control Systems
• Dynamic Analysis
• Introduction
• Structure description of arbitrary control systems
• Library of mathematical models of typical dynamic links
• Algorithms of forming and solving of mathematical model
• Examples
• References
• Software HYDRA
• Drives and Transmissions
• Dynamic Analysis
• Introduction
• Structure description of arbitrary hydro mechanical circuits
• Classification of drive base elements and their nodes
• Structure analysis of hydro mechanical drives
• Reduction of inertia moments and transfer attitudes
• Library of base elements and mathematical models
• Modeling of blocking mode
• Blocking of friction clutches and hydraulic torque converters
• General case of blocking of arbitrary number of clutches
• Algorithms of forming and solving of drive mathematical model
• Form of the analysis results presentation
• Example: simulation of dynamics of hydraulic transmission of self-propelled chassis
• References
• Software DRIVE