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Файл:Integrational mechanics. Lecture and exercises
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1.3. Methods of creation in integrational mechanics 11
4. Formulation of expected experimental results.
5. Final creation of an experimental results “field”.
Stages of search for analytical solution:
1. Revealing analytical contradictions among module problems.
2. Searching analytical unity of interconnected problems.
3. solving basic module problems using the consistent solving algorithms.
Stage of developing synthesized analytical solutions:
1. Complex usage of dialectical laws.
2. Justification of the common “base” of support solutions.
3. Creation of a control module as an additional informational to the above
mentioned “base”.
4. Development of modified opposite solutions on the base of the entire problem control module.
5. Creation of synthesized analytical theory with complex application of dialectical laws.
6. Validation of the created synthesized theory for “perfection” and for searching solutions reduced to support ones.
The examination of the created theory for a “perfection” includes the fol-
lowing points:
1. Taking into account the psychology of a designer or an engineer.
2. Possibility of turning harm into a benefit without design solutions.
3. Integration of some design problems by means of a common solution.
4. Validation of created synthesized theory for the novelty in terms of support
solution.
Stages of working out practical recommendations using a decimal matrix
of searching for invention problem solution:
1. Improvement of object geometrical parameters.
12 Chapter 1
2. Checking the improvement of physical and mechanical characteristics
(weight of a structure, weights of the separate elements, material consumption, strength, stability etc.).
3. Energy characteristics.
4. Design and technology characteristics.
5. Reliability and durability.
6. Operation characteristics.
7. Economical characteristics.
8. Standardization and unification factors.
9. Maintenance and safety factors.
Basic groups of system operators
System operators and system mechanics techniques may be subdivided into
six groups:
1. Information operators for overall analysis (a general information operator
of a null action).
2. System operators for quantitative estimation (a basis operator of classical
mechanics and others).
3. Operators of an informational channel (a dialectical system of coordinates,
an informational plane, an informational matrix, a block of informational
matrices).
4. Operators for developing information (ideal information, ideal theory, sliding theory, basis information, information pyramid, null-vector of information, reserve vector of information, information vector considered in a
dialectical contradiction, bifurcation coordinates, digitized vector of information, gen of information).
5. Combined system operators (block of an informational search, control module).
6. Operator of complex analysis of an object considering peculiarities of loading (analytical and design algorithm).
1.3. Methods of creation in integrational mechanics 13
Information operators for overall analysis
The operators for overall analysis realize the qualitative approach of system
analysis. There are two operators in this group. The first one is a neutral operator
which does not concern with a given object. It helps to examine mathematical,
physical and system (dialectics, methods of searching new ideas using a system
approach) components of a formula, a law, a phenomenon. This operator and
it three components are shown in Fig. 1.1. Graphically it is represented by a
formal plane. The operator is of practical significance for classical mechanics
studying.
GENERAL INFORMATION OPERATOR
components
MATHEMATICAL
Figure 1.1. General information operator
PHYSICAL SYSTEM
The second operator of a given group is an information operator of a null
action, which contains the same three components (see Fig. 1.2). But in this
case every component should be equal or not equal to zero. Every phenomenon
or object possesses its own information dealing with such a zero condition. For
classical mechanics:
• Mathematical component is represented by the mathematical condition that
a right part of an information equals a left part.
• Null is a “reference point” for information.
• Equality to zero in physical component represents the conservation of phys-
ical state of an object, i.e. homogeneity of an object’s material (rigid body,
deformable body; liquid).
• Gaseous uniform state), and also physical null, i.e. equilibrium conditions
for a system, an object.
• Dialectical component compressing an information related to the object
which is not physically changed.
14 Chapter 1
g;;S e
Figure 1.2. Information operator of null action
Operators for quantitative estimation
These operators arise when a general information operator applies for a
given object.
Fig. 1.3 illustrates a basic operator of classical mechanics:
• Mathematical component is represented by two opposite mathematical op-
erators of differentiation and integration.
• Physical component gives laws of conservation (=0) and laws of variation
(=0).
• System component is represented by a dialectical spiral of cognition.
Sign “.” designates a discrete unit of mass, unit of force.corresponds
to a force system, system of moments etc.designates center of mass, center
of gravity, center of inertia, resultant of a force system, principal vector of
moments etc. Such quantitative operators may be easily created for other parts
of mechanics.
Operators of an informational channel
They are:
• an informational matrix,
• a block of informational matrices,
• a dialectical system of coordinates (see Fig. 1.4),
• informational planes (Fig. 1.5) which rotate about a fixed axis.
1.3. Methods of creation in integrational mechanics 15
Figure 1.3. How a basic operator of classical mechanics is formed
Figure 1.4. Dialectic system of coordinates
In the two latter cases for each coordinate properties of an object on the left
side and on the right side must be mutually opposite.
Operators for developing information
This is a large group of operators. It includes both the operators dealing
with action and “operators – notions”.
16 Chapter 1
deformable body
statics
instability
Figure 1.5. Information planes
rigid body
stability
dynamics
Operators for developing information:
• ideal information (compression, compactness of the information, ability of
using information for other parts of an object, dialectical unity);
• ideal theory, its basic attributes are: simplicity, enough amount of an information, overcoming of a signification, support solutions, turning harm into
benefit, system organization of the theory creation;
• sliding theory – it can be treated as some “tangent” to an information block,
it contains a qualitative information and helps to obtain finally a true information for our process;
• basic information, i.e. fundamental information determining an object, an
information cannot be compressed further; in classical mechanics such an
information is a force and a moment of force; in mechanics of a deformable
body – a wave of expansion and a wave of shear; in dynamics — a mass
and a displacement; thus, a basic information depends on an object and the
problem to be solved;
• informational trumpet (see Fig. 1.6) is formed by the components of an information operator, i. e. this is another way of representation of the general
information operator, with dashed indication of information ribs;
• informational pyramid is a principal operator of forming information.
Fig. 1.7 and Fig. 1.8 illustrate two basic pyramids: integral mechanics,
1.3. Methods of creation in integrational mechanics 17
mechanics as an object in the unity of all its problems, each pyramid side
is a information plane; pyramid of integral mechanics of an object (see
Fig. 1.8) is one side of the informational pyramid (see Fig. 1.7) built on the
base of general information operator; an inverse information pyramid (see
Fig. 1.9) is a practical case in which an information is compressed in each
side to produce the main information for the object;
• null-vector of information; this operator is convenient for the qualitative
analysis;
• the notion of a mathematical null, i. e. of null-vector, is a mathematical
component of this operator;
• reserve vector of information, it is used for the system finishing of principles of classical mechanics;
• information vector considered in a dialectical contradiction can be represented, for instance, by informational axes (see Fig. 1.4);
• bifurcation coordinates are invented for the analysis of informational pyramid ribs when the mathematical unity of system mechanics of an object is
considered; they are used in a system mathematics;
• digitized system of information compresses an information and translates it
in the form of an object.
mathematics
physics
Figure 1.6. Informal trimpet
dialectics
18 Chapter 1
y
Figure 1.7. Integral mechanics pyramid built up on the base of general information
operator
statics
vibration
stabilit
impact
Figure 1.8. Pyramid of system mechanics of
an object
Figure 1.9. Reverse information
pyramid
Combined system operations
The three last typical procedures of integrational mechanics are reserve
vector of information, it is used for system finishing of principles of classical mechanics; referred to combined system operations. The generation of a
module for control of complex problem solving process is beyond formality. If
a problem of impact is under consideration, then a theoretical solution of the
problem for an impact loading is the base of information pyramid; and theory
of vibration, theory of stability, theory of statics are the sides of the information
pyramid. The peculiarity of a “strong” module for control is that each module
problem is in turn a whole problem. The most important information obtained
from the module problem and verified by an experiment, carries an information
gen of this problem. Our main purpose is to observe how an object is divided
1.4. Classification according to the type of nonlinearity 19
onto theoretical description and experimental phenomena, and how it is simultaneously rebuilt with help of the information gens. The gens of module problems
completing each other are collected in unit hypothesis. The procedure of development of the module of “ideal theory” is taken from the methods of an technical
creation [3], but it is adapted for the problems of dynamics and strength, and
for applied mathematics. The method of plausible reasonings [4] stating that to
solve the problem one should know the answer, is used in this procedure. The
attributes of an “ideal theory ” are: simplicity, enough amount of information,
overcoming of a significant contradiction, support solutions, turning harm into
benefit, system organization of the theory creation.
The most powerful procedure is a complex procedure of a system analysis
(see Fig. 1.10.), it incorporates a module of control, an “ideal theory”, and a
complex method of dialectics laws usage. From module problems one use the
modules being the sides of information pyramid, and create a module of control.
Two mutually opposite theories using the same experiment field one extracted
from the common base of solution. The chain “common base of the solution”,
“positive theory ”, “experimental result field” corresponds to the law of quantity and quality. The second chain of replacement of a “positive theory” by a
“negative one ” and of their synthetics corresponds to the law of interaction of
opposite entities. Both theories correspond to the law denial by denial. Besides
the principle of extension of “positive” and “negative” theories beyond fields of
their applications realizes K. Marx‘s methodology of a contradiction analysis.
1.4. Classification of mechanics problem according to the type
of nonlinearity
The general information operator can be applied for classification of prob-
lems according to the type of nonlinearity (table 1.1.).
Using such an approach we distinguish three types of nonlinearities: mathematical nonlinearity, a nonlinear problem has the only solution (there is no
bifurcation of solution); physical nonlinearity (geometrical, physical, instability
of motion etc.), a nonlinear problem has a set of solution (there is a bifurcation
of solution); system nonlinearity, a real problem is equivalent to a number of
problems with different physics of the phenomenon (there is a bifurcation of
problems).
System and nonlinear problems, and blended problems can have both combinations of different physics; vibration – statics, vibration – stability, vibration – impact, statics – stability, statics – impact, stability – impact. A system
object – interconnected nonlinear problems denoted conditionally by sign.
20 Chapter 1
Unit object. Unit physics of object
Figure 1.10. Integrational mechanics of object as a common structure of mathematics,
physics and applied philosophy of object
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