Articles and Publication  Physics Theoretical physics INTRODUCTION TO MECHANODYNAMICS
INTRODUCTION
TO MECHANODYNAMICS
©
Ph. M. Kanarev.
Contact
to the author: kanphil@mail.ru
Announcement.
Newton’s
dynamics operated within 322 years with the vivid features of a violation of the
cause and effect relationships originating from its first law. A transition of
dynamics into the framework of the cause and effect relationships has proved to
be possible only when the new scientific notions have been introduced and its
laws have been systematized.
_______________________________________________________________________
THE
FIRST LECTURE
1. General Date concerning mechanodynamics
A
notion of “Dynamics” was introduced long ago and acquired various prefixes,
which limit a sense laid down in this notion, and give more concise reflection
of a gist of the phenomena and process being described. The notions of “Electrodynamics”,
“Hydrodynamics” and “Aerodynamics” have been used long ago. A notion of
“Electrodynamics of microworld” has appeared. As a result, it has become
necessary to distinguish dynamics, which describes mechanics of rigid bodies
only. Taking it into account, we introduce a notion of “Mechanodynamics”,
which lays down a sense of dynamics of mechanical motions of rigid bodies, which
have been described by the notion “Dynamics” prior to it.
“Mechanodynamics”
is a part of theoretical mechanics, in which a relationship of a motion of the
material points and bodies and the forces exerting influence on them is
established and studied.
A
material point and a perfect rigid body are the main models of the actual
objects in mechanodynamics. Such actual objects, which variations in a motion of
the separate points can be neglected, are considered as the material points. If
it is impossible to do it, a motion of such object can be considered as a motion
of a rigid body.
A
perfect rigid body is a complex of the material points, the distances between
which are not changed in length of time. It appears from this that a material
point is a particular case of a rigid body.
A
complex of the material bodies, in which they cannot move independently from
each other due to the relationships between them, is called a mechanical system.
The
laws of mechanodynamics are based on the fundamental axioms of natural science:
space and time are absolute; space, matter and time are inseparable. An
authenticity of the axioms originates from obviousness of their statements. An
authenticity of the laws of mechanodynamics, which are based on the axioms, is
non-obvious and is proved experimentally; that’s why of the laws of
mechanodynamics cannot be considered the axioms, they are postulates.
For
the first time, the laws of dynamics were systematized by
Isaac Newton in his book “Mathematical Principles of Natural Philosophy”
(1687).
He formulated the first law of dynamics
in the following way:
“Every
body continues in its state of rest, or of uniform motion in a straight line,
unless it is compelled to change this state by forces impressed upon it”. In
this statement, we see at once a
violation
of the principle of the cause and effect relationships. Any motion is a cause of
an action of a force, but it is missing in Newton’s first law; there is no
mathematical model of this law, which describes its constant movement in space,
but a body ignores it and moves with constant velocity
 (Fig.
1, position A). The discrepancies being described are a cause of a violation of
the principle of sequence of an analysis of the phenomenon or the process being
described. This principle requires
a description of the process or the phenomenon from its very beginning, not from
the middle. An accelerated motion is the beginning of any motion, and a uniform
motion is its cause. Thus, in order to return the principle of the cause and
effect relationships into the former Newtonian dynamics, it is necessary to put
the law of the accelerated motion of a body to the first place. As a result,
we’ll get a new dynamics. In order to differentiate it from the old dynamics,
let us call it “Mechanodynamics”. It will describe only mechanical motions
of the bodies. The centuries-old experience of the use of Newton’s second law
has proved its irreproachable authenticity; that’s why we have every reason to
put it in the first place and to call it the main law of mechanodynamics.
Fig.
1. On analysis of the law of mechanodynamics
a)
diagram of appearance of the forces acting on asteroid A, which approaches
planet M;
b) diagram of a change of resistance forces
acting
on a body having the accelerated motion (OA), a body having the uniform motion (AB)
and a body having the decelerated motion (BC)
2.
Main Law of Mechanodynamics
Force
acting
on a material body, which moves with acceleration
,
is always equal to mass
of
the body multiplied by acceleration and coincides with an acceleration direction
(Fig.
1, a
, position 2).
(1)
In
order to discriminate force
,
which forms acceleration, from other forces, let us call it Newtonian force. It
always coincides with the direction of acceleration
,
which it forms. All other forces are the motion resistance forces.
In
1743, Jean d’Alembert supplemented this Newton’s law having mentioned that
the inertia force
,
which is directed conversely to the acceleration direction
and
is equal to
(2)
It
appears from this that two forces, which are equal in their values and opposite
in their direction, act on the body, which moves with acceleration, in each
given instant of time: Newtonian force
and
d’Alembertean inertia force
.
Newtonian force
acting
on asteroid A, which approaches planet M, and the inertia force
directed
oppositely to Newtonian force are shown in Fig.
1, a
, position 2. As there are no mechanical resistances in space, equality of
these forces should bring the body in a quiescent state or in a steady motion
state, but it moves with acceleration proving a discrepancy of such notions and
demanding their elimination.
3.
The First Law of Mechanodynamics
For
more than 300 years, it was supposed that Newtonian force
moves
a body, and a sum of resistance forces
 hinders
this motion without a participation of the inertia force
,
which is also directed oppositely to the motion (Fig. 2, b). In order to make
certain of erroneousness of such an approach to the solution of the problems of
mechanodynamics, let us consider the accelerated motion of a car in detail (Fig.
2, b).
Fig.
2. Diagram of the forces acting on a car, which moves with acceleration (OA)
Each
of us goes by car and knows that when it moves with acceleration, the inertia
force presses us to a squab. If other car hits our car from behind, the
acceleration can be such that strength of the muscles of our body and resistance
power of the neck vertebra will be less than the inertia force, which carries
our head back. A head-rest helps to save us from the inertia force, which is
capable to tear off our head. If our car runs into an obstacle, which suddenly
appears before the car, the acceleration of its motion will be changed for aò
opposite one and will turn into a slow-up being directed
against the motion of the car, and the inertia force will act in the direction
of the car drive. In order to prevent this force from throwing us through a wind
shield, we fasten the belts.
Thus,
the authenticity of the described process of an appearance and a change of the
inertia was proved by millions of lives of the passengers who perished in the
road accidents when the cars were driven, but the physicists and
fitters-theoreticians go on ignoring it thinking that the inertia force
is
not among the forces
acting
on the body during its accelerated or decelerated motion. Let us correct their
mistake.
When
a car moves with acceleration (Fig. 2. b), the following forces act on it:
Newtonian force
being
generated by its engine, the inertia force
directed
oppositely to the acceleration
of
the car and arresting its motion, an aggregate force of all external resistances
,
which is also directed conversely to the direction of the car. As a result, we
have a conclusive equation of the forces exerting influence on the car, which
moves with acceleration (Fig. 2, b).
 .
(3)
This
is the first law of mechanodynamics.
It reads: the accelerated motion of a
body takes place under the influence of Newton’s active force
and
the motion resistance forces in the form of the inertia force
and
the mechanical resistance forces
.
If
we agree with d’Alembert who thought that the inertia force value è
is
equal to the body mass
multiplied
by the same acceleration
,
which takes place under the influence of Newtonian force
,
the resistance force
being
a part of the equation (3), equals zero. There is only one way from this
contradiction: it is necessary to introduce the notions of a force, which
generates acceleration
,
and a force, which generates deceleration
.
Thus, Newtonian force
will
always generate acceleration
,
and all other forces will generate deceleration. We have every reason to think
that Newtonian force
coincides
with the acceleration
direction,
and the forces, which hinder the motion and, consequently, generate deceleration,
coincide with the direction of decelerations
being
formed by them (Fig. 2, b). If we designate the deceleration, which belongs to
the inertia force, via
and
the deceleration, which is generated by the forces of mechanical resistances
,
via
,
we can rewrite the equation (3) in the following way
.
(4)
It
is easy to see that in case of a complete absence of the forces of mechanical
resistances
(for
example, in space), the inertia force
equals
Newtonian force
,
but the body is moving. It is possible only in case when Newtonian force exceeds
the inertia force; that’s why a mathematical model, which describes a motion
of the body in space, should be presented in the form of an inequality
,
(5)
or
.
(6)
This
is a condition of the body motion in space in case of resistance absence. It
appears from this that an actual inertial deceleration
of
the body can be determined under the conditions when there are no external
resistances. It is natural that the specialists in space engineering are in
possession of the methods of such determinations and have experimental
information concerning it.
Thus,
a value of complete acceleration
of
the body, which moves with acceleration, equals a sum of the decelerations being
generated by the motion resistance forces.
(7)
In
old dynamics, an inertial component of deceleration
was
a part of a deceleration
being
generated by the forces of mechanical resistances to motion; it hindered an
analysis of the forces acting on all types of motions: accelerated motion,
uniform motion and decelerated one. It was considered that the inertia force
,
which also hindered the accelerated motion of the body, was not a part of the
sum of all forces of mechanical resistances
.
It is the main fundamental error of Newtonian dynamics, which has remained
unnoticed during 322 years. Automatically, the inertia force was a part of the
aggregate force of mechanical resistances
,
but everybody thought that it was not there. As a result, all experimental
coefficients of mechanical resistances to body motion prove to be erroneous.
It
appears from the equation (4) that the inertia force
,
which acts on the car when it moves with acceleration, equals
,
(8)
and
a scalar value of inertial deceleration
is
determined according to the formula
. (9)
A
value of complete Newtonian acceleration is determined from the kinematical
equation of the accelerated motion of the body
 .
(10)
If
the initial velocity of the car
is,
complete acceleration
equals
velocity of the car
at
the moment of its transition from the accelerated motion to the uniform motion
divided by time of the accelerated motion.
.
(11)
In
principle, when the problems are being solved, it is possible to assume that a
value of velocity
equals
a value of constant velocity (
)
of the body during its uniform motion, which takes place after the accelerated
motion. A sum of the resistance forces
is
an experimental value, which should
be determined only in case of uniform motion in order to exclude the inertia
force from it.
Thus,
all the data, which are necessary for a determination of inertial deceleration
and
a calculation of the inertia force
according
to the formula (8), are available. It appears from this formula that a fraction
of inertial deceleration
depends
on the medium resistance
(9).
If
it is necessary to determine the body motion resistance forces, it should be
done only during its uniform motion. If a sum of the body motion resistance
forces
is
determined during its accelerated motion, the inertia force
,
in accordance with the formula (3), is automatically included in the sum of the
motion resistance forces
, and a result of the determination of resistance forces will be
completely erroneous.
4.
The Second Law of Mechanodynamics
When
the car begins uniform motion (Fig. 3, b), the inertia force
changes
its direction for the opposite one automatically, and the equation of the sum of
the forces (3), which act on the car, becomes as follows:
.
(12)
Fig.
3. Diagram of the forces acting on the car, which motion is a uniform one
This
is the second law of mechanodynamics
- the law of uniform motion of the body (the former first law of Newtonian
dynamics). It reads: if there are no
resistances, uniform motion of the body (Fig.
1, a
, position 1) takes place under the influence of the inertia force
.
If there are resistances, uniform motion of the body takes place under the
influence of the inertia force
as
well, and the constant active force
overcomes
the motion resistance forces
(Fig.
3, b).
Thus,
the essence of the second law of mechanodynamics is in the fact that uniform
motion of the car (body) is provided by the inertia force
,
and the constant force
being
generated by the car engine overcomes all external resistances
.
The force
is
constant, because the car has uniform motion, and its acceleration equals zero
.
In
space, where there are no mechanical resistances to motion, constant force for
their overcoming is not required. That’s why when the body changes its
accelerated motion for uniform motion, the inertia force changes its direction
for the opposite one and hereby provides its uniform motion with constant
velocity
(Fig.
1, position 1).
Again,
let us pay attention to the main centuries-old error of the mechanicians. For
this purpose, let us rewrite the equation (12) in the following way:
,
(13)
This
is a mathematical model of the second law of mechanodynamics (the former first
law of dynamics). There was no mathematical model for a description of uniform
motion of the body for more than 300 years. Now it exists (12), (13).
Now
we can set pilots' mind at rest. Uniform flight of their plane is described by
the second law of mechanodynamics (12). According to this law, a sum of the
forces, which act on the plane having uniform motion, does not equal zero (13).
A force, which provides uniform motion of the plane, is the inertia force, which
was directed oppositely to its motion when it moved with acceleration (took off).
When the plane begins uniform motion, the inertia force changes its direction
for the opposite direction and coincides with a force being created by the
engines of the plane. As a result, the inertia force begins to provide a uniform
flight of the plane, and the forces of the engines of the plane begin to
overcome the resistance forces to its flight. Thus, the uniform flight of the
plane is governed by the second law of mechanodynamics (12), according to which
a sum of the forces acting on it does not equal zero.
5.
The Third Law of Mechanodynamics
It
is necessary to have a clear idea concerning a change of the direction of the
inertia force when a transition from uniform motion to decelerated motion of the
body (car) takes place. When the car changes its uniform motion for decelerated
motion, the primary inertia force
(Fig.
4, b) does not change its direction, and the deceleration
,
which has occurred and is generated by the resistance forces, is directed
opposite to this force.
Fig.
4. Diagram of forces acting on the car, which has decelerated motion
Thus,
if the car changes its uniform motion for decelerated motion, the former inertia
force
and
the motion resistance forces
do
not change their directions. The inertia force does not generate acceleration,
and irregularity of the resistance forces results to a gradual reduction of the
inertia force
,
and the body stops.
.
(14)
This
is a mathematical model of the third law
of mechanodynamics. It reads: decelerated
motion of a rigid body is governed by exceeding the motion resistance forces
over the inertia force.
If
a speed-box of the car is cut off, active force disappears
(Fig.
3, b), and two oppositely directed forces remain: the inertia force
and
a sum of forces of mechanical resistances to motion
(Fig.
4, b). As the inertia force has no source, which keeps it in a constant state,
it proves to be less than the motion resistance forces (
),
and the car, which begins decelerated motion (Fig. 4, b), stops (Fig.
4, a
, point C). Taking it into account, we have every reason to call the inertia
force a passive force, which cannot generate acceleration, because it is a
consequence of its emerging.
Let
us pay attention to the fact that a distance
of
the car motion with acceleration is less than a distance of motion with
deceleration
(Fig.
4, a
). It is stipulated by the fact that a value of the resistance forces
in
case of acceleration from stop on the part
exceeds
the resistance forces in case of decelerated motion due to the fact that in case
of decelerated motion the engine and the speed-box are cut off. This is the main
reason of fuel conservancy when the car moves with a periodic speed-box cutoff.
6.
The Fourth Law of Mechanodynamics
The
fourth law
of mechanodynamics (There
is always an equal and opposite reaction to every action): the forces, with
which two bodies act on each other (Fig. 1, à,
pos. 2), are always equal according to the modulus and are directed in a
straight line, which connects the centres of masses of these bodies, to the
opposite directions.
In
the second position of Fig.
1, a
, it is clear that force
of
action of planet M equals
,
and force
of
action of asteroid A on planet equals
(
-
accelerations of the asteroid and the planet, respectively). As
, it means that
or
(15).
It
means that the accelerations, which two bodies give each other, are inversely
proportional to their masses. The accelerations are directed along one and the
same line to the opposite directions. It should be noted that the fourth law of
mechanodynamics reflects an interaction of the bodies both at a distance (Fig.
1, a
, position 2) and in case of a direct contact (Fig. 5). It is shown in Fig. 5
that when the bodies A and B contact each other, the forces of their interaction
and
are
equal in their value and are opposite in the direction. Both forces
and
are
the forces of external impact, and they emerge simultaneously.
Fig. 5. Diagram of
contact interaction of two bodies
The
inertia forces
and
are
equal in their value and opposite in the direction.
7.
The Fifth Law of Mechanodynamics
The
fifth law of mechanodynamics (independence of action of the forces). If several
motion resistance forces
=
act
simultaneously on a body or a point, Newtonian acceleration
of
the material point or a body is equal to a geometrical sum of decelerations
befalling to each motion resistance force
=
.
Taking into account that in the equation (7)
the
geometrical sum of decelerations befalling to all resistance forces is
=
,
except the inertia force
,
i.e.
.
The equation (7) can be written in such a way:
(16)
This
is a mathematical model of the fifth law
of mechanodynamics. It reads: when
a rigid body moves with acceleration, Newtonian acceleration being forms by
Newtonian force equal a sum of decelerations being formed by all motion
resistance forces.
Let
us recollect Galileo’s experiment, in which he placed the bodies having
different masses and densities in a tube. He pumped air out of it, and it turned
out that if the tube was placed vertically, all bodies fall down at the same
rate. As in accordance with the main law of mechanodynamics the force acting on
the body equals a product of mass by acceleration, it seems that the bodies
having different masses should move with different rates, but it is not
observed. Why?
Fig.
6. Diagram of action of the forces on the bodies, which move in the evacuated
tube
If
only one force of gravity
acted
on the bodies in the evacuated tube (Fig. 6), each body would move at a
different rate; but as all of them move at the same rate and with one and the
same acceleration, two forces act on each of them: force of gravity
and
inertia force
.
Accelerated motion of each of them points out to the fact that force of gravity
exceeds inertia force
.
Thus, we have:
.
(17)
As
,
(18)
mass
of a material body equals to its weight
divided
by free fall acceleration in a given place of the surface of the earth.
As
a force measurement unit in SI system, a Newton is accepted (N). One
Newton force is that force which produces an acceleration of 1 m/s2.
In
technical unit system,
1 kg
is accepted as a force measurement unit, and
1 kg
×m/s2
is
accepted as a mass measurement unit. As
,
it means that 1 kg=1×9.81
N or 1 N=0.102 kg.
New
knowledge in the field of mechanodynamics makes it possible to determine exactly
the resistance forces to motion of any body. A determination method of these
forces results from the formulas (3-11). If the car motion resistance forces are
determined, it is necessary to choose a uniform horizontal part of the road, to
drive a specified distance along it with a specified constant velocity and to
measure fuel consumption. Energy of this fuel will be equal to work of a force
,
which counteracts all motion resistance forces
,
at the registered part of the road. It appears from this that the force
is
equal to a sum of forces
.
If
a similar experiment is carried out at an accelerated motion of the car, the
inertia force
,
according to the formula (3), which hinders an accelerated motion of the car,
will be automatically included in the sum of resistance forces
,
and a result of the resistance force determination will be completely erroneous.
Newtonian
or motive force will be determined in accordance with Newton’s second law
.
(19)
In
this case it is more convenient to determine Newtonian acceleration
according
to the formula (11) and an inertial component
according
to the formula (9). The inertia force will be determined according to the
formula (8).
THE
SECOND LECTURE
MECHANODYNAMICS OF CURVILINEAR ACCELERATED MOTION, UNIFORM MOTION AND
DECELERATED ONE OF A MATERIAL POINT
1. Mechanodynamics of Accelerated Curvilinear Motion of a Point
A
curvilinear motion of a point is usually described in a natural system of
coordinates, which has a normal axis
,
a tangential axis
and
a binormal
(Fig.
7). A plane
is
called an osculating plane. The axis
is
perpendicular to the osculating plane. Velocity
of
the point is directed along the motion.
Fig.
7. Diagram of accelerations and forces acting on the material point, which moves
curvilinearly
and with acceleration
As
the motion is a curvilinear one, a normal component
of
complete acceleration
is
always directed to a concavity of the curve (Fig. 7). A direction of the
tangential component
of
complete acceleration
depends
on a nature of the curvilinear motion. If it is accelerated, the directions of
the tangential acceleration
and
a velocity vector
coincide
(Fig. 7).
As
a motion is an accelerated curvilinear one, the following forces act on the
material point: Newtonian (active force)
,
a sum of resistance forces
directed
oppositely to the motion, the tangential component
and
the normal component
of
complete inertia forces
.
A vector of Newtonian force
is
directed along a vector of complete acceleration
to
the concavity of the curve. It is decomposed into two components: the normal
component
and
the tangential one
.
As
the tangential inertia force
is
directed oppositely to the acceleration
,
the normal component
of
the inertia force is always directed from the from the trajectory curvature
centre along a curvature radius, and the tangential component
of
the inertia force is directed oppositely to the tangential component
of
the complete Newtonian acceleration
and
coincides with a direction of the tangential deceleration
.
Thus,
an equation of the forces, which act to the material point along a tangent to
the curvilinear trajectory, will be written in the following way
(20)
or
.
(21)
As
it is clear, the equations (20) and (21) are similar to the equations of the
forces (3) and (4) acting on a body, which moves with acceleration in case of a
straight-line motion. In order to solve this equation, it is necessary to know
acceleration
and
deceleration
.
In order to determine them, it is necessary to know primarily a point motion
equation. In the case being considered, it is preset in a true form
.
(22)
When
we know the point motion equation (22), we find its velocity
(23)
and
the tangential acceleration
.
(24)
A
normal acceleration modulus
is
determined according to the formula
,
(25)
where
is
a trajectory curvature radius.
A
deceleration modulus
can
be determined only in the case when a sum of the resistance forces
,
which act on the point, is known. The value
is
determined experimentally. If we know it, we find a deceleration
,
which is formed by the tangential component
of
the inertia system (Fig. 7).
.
(26)
It
appears from this equation that the deceleration
,
which falls to the share of the resistance forces
,
is equal to
(27)
or
.
(28)
Thus,
new laws of mechanodynamics make it possible to describe a process of the
accelerated curvilinear motion of the material point correctly. Let us describe
a uniform curvilinear motion of the point.
2.
Mechanodynamics of Uniform Curvilinear Motion of a Point
In
case of the uniform curvilinear motion of the point, the tangential acceleration
equals
zero, but a tangential force of inertia
,
which acted on the point when it moved with acceleration prior to a transition
to a uniform motion, does not disappear anywhere. It changes its direction to
the opposite one (Fig. 8). As a result, a sum of the tangential forces, which
act on the material point, will be written in the following way
.
(29)
Fig.
8. Diagram of the forces acting on the material point in case of the uniform
curvilinear
motion
Let
us remind that the sum of the point motion resistance forces
is
an experimental value. As velocity of the curvilinear motion of the point is a
constant value
in
this case, the tangential component of its complete acceleration
equals
zero
,
and there remains only the normal acceleration
,
which corresponds to the normal component of the inertia force
directed
oppositely to the normal acceleration (Fig. 8).
A
physical essence of the equation (29) is as follows. The active tangential force
overcomes
all motion resistances
,
and the inertia force
moves
the point uniformly. Thus, we have all the information being necessary for a
determination of the forces acting on the material point, which moves
curvilinearly and uniformly.
3.
Mechanodynamics of Decelerated Curvilinear Motion of a Point
When
a material point changes its uniform motion for a decelerated curvilinear
motion, a tangential component
of
the active force disappears. There remain a tangential component
of
the inertia force and the sum of the motion resistance forces
,
which generates a deceleration
(Fig.
9). As the sum of the motion resistance forces
exceeds
the inertia tangential force
,
which does not generate acceleration, the deceleration
,
which corresponds to force
and
coincides with its direction, forms together with the acceleration normal
component
a
complete acceleration
directed
from the left side of the normal axis
(Fig.
9).
Fig.
9. Diagram of accelerations and forces acting on the point in case of its
decelerated
curvilinear
motion
When
the point passes to a decelerated motion, the sum of the motion resistance
forces
exceeds
the inertia force
,
and the motion of the point is decelerated gradually.
New
knowledge in the field of mechanodynamics makes it possible to determine exactly
the resistance forces to motion of any body. A determination method of these
forces results from the formula (29). If the point motion resistance forces are
determined, it is necessary to do it only when it moves uniformly. If the sum of
the point motion resistance forces
is
determined in case of its accelerated motion, the inertia force
,
in accordance with the formula (29), which hinders the accelerated motion of the
point, will become a part of the sum of the motion resistance forces
automatically,
and the result of the determination of the resistance forces will be erroneous
completely.
In
case of the curvilinear motion, Newtonian, or active, force is determined
according to Newton’s main law
.
(30)
Complete
Newtonian acceleration
is
connected with its normal component
and
the tangential one
by
simple dependence
,
(31)
That’s
why if
and
are
known, it gives an opportunity to determine complete acceleration
.
Let
us note that if the radius of the point motion trajectory curvature is constant,
all the facts, which are described in this lecture, belong to a motion of the
point in a circle as well.
CONCLUSION
These
two introductory lectures in mechanodynamics have enough information for a
review of all other parts of Newton’s old dynamics. The specialists in
theoretical mechanics will understand an essence of the first two lectures and
will write all other ones without our participation. But if they fail to
understand the essence of erroneousness of Newton’s first law, erroneous
dynamics will exist for a long time.
New
laws of mechanodynamics have
already allowed us to describe in details process of a shot of second power unit
Sajano-Shushenskoj of HYDROELECTRIC POWER STATION. The sum of forces of
resistance to power unit movement exceeded
.
Physical and chemical process in a
water delivery zone on
the turbine blade has generated the shock force equal EMBED
Equation.3
Results
of calculation of pulse force by means of laws mechanodynamics
coincide
on 93 % with calculations of this force
by means of laws of physchemistry of processes which have
generated by this force.
REFERENCES
-
Kanarev
Ph.M. The Foundation of Physchemistry of Microworld. Monography.
http:/kubsau.ru/science/prof.php?kanarev
+
English
-
Kanarev
Ph. M. MECHANODYNAMICS OF SAJANO-SHUSHENSKY
TRAGEDY
http:/www.sciteclibrary.ru/rus/catalog/pages/10145.html
Publishing date: February 25, 2010
Source: SciTecLibrary.ru
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