2.0. Theoretical completion of Coriolis' acceleration formula and its practical applications
2.1. Derivation of completed formula of Coriolis' acceleration
X"1 = ![Omega [Владимир Суханов]](/img/s/suhanow_w_n/2koren/omega.jpg){kind=small}
X'(2X-dX) / (X-dX) ;
X"2 = X'(2X+dX) / (X+dX) ,
- angular velocity of rotating of frame of reference,
X"1 = - X"2 (e.g. X" changes its own sign on contrary) when the material point has just crossed the centre of rotation. For the formula X"2 at negative value X: X"2 = - X"1. The formula X"2 can be got by following manner. In accordance with the Energy Conservation Law, energy E of the material point, when X' = const and
= const, equal sum of energies and has its constant value:
E = Ex + Ev + E + Ek = const
where
- work which is made by centrifugal and centripetal forces, when of the material point displaces,
Ex = M(X')2 / 2
Ev = Mv2 / 2
E = M X"cX
Ek = M X"2l
dEv + dE + dEk = 0
since
dEx = 0 if M(X')2 / 2 = const.
Here:
dEv = M(v+dv)2 / 2 - Mv2 / 2
or
dEv = M(v2 + 2vdv + dv2 - v2) / 2 = M(v + dv/2)dv
where
v = X , but dv = dX ,
dEv = M(X + dX / 2)2dX ;
dE = M2(X + dX / 2)dX
where
(X + dX / 2)2 = X"c
dEk = M (l + dl)X"2 ,
where
l = vT or l = XT
dl = Tdv or dl = TdX ;
or
dEk = M X"2(XT + TdX) .
or
dEk = M X"2 T(X + dX) .
Consequently
M X"2T(X + dX) = M2 (X + dX / 2)dX + M2 (X + dX / 2)dX
where
dX / T = (X')
from this
X"2 = V(2X + dX) / (X + dX)
dEv = M[(v - dv)2 - v2] / 2
dE = M2(X - dX / 2)dX
dEk = M X"1T (X - dX)
, e.g. that is frame of reference has itself angular acceleration of equal-slowing rotation ![Epsilon [Владимир Суханов]](/img/s/suhanow_w_n/2koren/epsilon.jpg){kind=small}
.
In first case, when X"
![Neravno [Владимир Суханов]](/img/s/suhanow_w_n/2koren/neravno.jpg){kind=small}
0, new component of energy arises in the equation of energy E:
Ex = MX"X , here dEx = MX"dX
From equation
dEx + dEv + dEk + dE = 0
it can be obtained next formula:
X"2 = [(X' + X"dX / X')(2X + dX) + X"X'/] / (X + dX)
X"1;2 = 2(X') :
X"1;2 = 2(X') + X"(X') / X
or
X"1;2 = 2(X') + k X"
X = v , and k = (X') / v is ratio of the linear relative speed to velocity of motion of the material point in a circle.
if X" / X = 22 , that X"1;2 = 0
0, new component of energy arises in the equation of energy E:
E = MXl
Then
dE = M(X + dX/2)(l+dl)
or
dE = MT(X + dX/2)(X+dX).
From equation
dEk + dEv + dE + dE = 0
it can be obtained next formula:
X"2 = (X' + X/2)(2X+dX) / (X+dX) .
X"1;2 = 2(X') + X
0 and 0 the formula take its next view:
X"1;2 = 2(X') + X + kX" .
X"2 = [(X'+ X"dX/ X'+X/2 +dX/2 +1)(2X+dX) + X" X'/)] / (X+dX)
or
X"2 = (X + dX/2) + [(X'+X"dX/X')(2X+dX) + X" X'/)] / (X+dX)
or
X"2=(X'+X"dX/X'+X/2+dX/2+2X"X'X/+X"X'dX/) (2X+dX)/(X+dX)
2.2. Acceleration of relative motion arising in rotating centre of frame of reference
X" = 2
X" =
X" =
(2X - dX) / (X - dX) = 2
X" =
The graphic 1. Acceleration of relative motion which arises in centre of rotation of frame of reference
2.3. Phenomenon of shock change of acceleration and its effects on flying apparatuses into the atmosphere mass
(X" ) = 2
X" = 2
Supplement 2. Coriolis Formula
Supplement 2.1. Theoretical completion of Coriolis' formula and some atmospheric reason of airplanes catastrophes
X2"=
X2"=
X"X' /
Supplement 2.2. Hydrological reasons of catastrophes of high-speed submarines
X2" =
The surrounding us world has lots of free energy and for it description and using it is not needed nay exotic and anomaly theories because we have still enough our knowledge for opening of large resources of the universe nature.
In the beginning of the 19-th century Gaspard-Gustave Coriolis, French mathematician, mechanical engineer and scientist, using kinematical principles and researching relative movement objects revealed and calculated acceleration and force, which arise when object moves into rotating frame of reference. Later the acceleration and the force were named after his name. Much time passed from that moment and science mechanics contains except static and cinematic else and dynamic but we, as kind latterly time, continue to calculate the Coriolis' force by the principle of cinematic.
I we observe motion of an object into rotating frame of reference using Energy Conservation Law, we got not exactly the same as Coriolis got. If we take
- X" - Coriolis' acceleration
That we can write the well know Coriolis' formula in next view:
And make its solution relating to the Coriolis' acceleration, that we can obtain
On a graphic it looks such:
Fig.
We can see the acceleration and, consequently, the force which exposes on the object have two segments, where the force aspires to infinity but on each of them to different directions so total energy of the object on observing segments does not change. But if we examine each segment of the object trajectory in separate, we reveal huge force which deflects the object from straight trajectory.
It is a surprise. Why not anybody has taken into consideration those huge forces? And why those forces are concealed? Conditions can arise in which overcoming of the concealed force can be as overcoming of thin armour. Its thickness aspires to zero. It is needed other armour, but thicker than one, for overcoming it. For example, not all flight apparatus have some armour. So space apparatuses turning back from orbit on the Earth with the first space speed can be destroyed absolutely because huge linear relative velocity X' when they meet with concentric movement the atmosphere. Similar catastrophes with airplanes and speed submarines we have known enough but full Coriolis' force is concealed for the majority specialists until now.
Examining numerous ways mechanical using of concealed energy, we can reveal that in some cases some inventors still use, intuitively, practically the Coriolis' force in it extremity. We can use the concealed force in its fully and with realization having this full Coriolis' formula.
Using principles of dynamic for determine of Coriolis' force open for us, as we could see, earlier unknown possibilities. What happen if we will use for calculation of Coriolis' force principle of relativity or quantum mechanic? We will be able to open much interesting things....
V
- angular velocity of rotation of frame of reference,
If a moving material point crosses centre of rotation of frame of reference that
V
V(2X - dX) / (X - dX)
where
In majority of cases X does not aspire to zero, consequently:
![Strelka [ Владимир Суханов]](/img/s/suhanow_w_n/2koren/strelka.jpg){kind=small}
dX acceleration X" aspires to infinity and exchanges its own sign in opposite. Coriolis' acceleration begins to act in opposite direction in comparison with usual. Farther, X" decreases to zero (for X0,5dX) and increases again. At motion through the centre of rotation (X=0) X"=V. When the material point going away from the centre of rotation, X'' aspires to 2V and if X reaches of a few dX that X" will be equal 2V already.
V(2X+dX) / (X+dX) (see graph).
![Graphyc [Владимир Суханов]](/img/s/suhanow_w_n/2koren/kor.gif)
Motion to the centre of rotation presents danger for mechanism (and for all) because of shock change of Coriolis' acceleration from normal to zero trough infinity with change its sign. Here destruction does not expel.
![ZOmega [Владимир Суханов]](/img/s/suhanow_w_n/2koren/zomega.jpg){kind=small}
, start to act upon the flying apparatus:
Vm
, and each relative motion in a moving of frame of reference has component of velocity V , which cross the metacentre. Coriolis' acceleration X" during motion in the moving atmosphere, which has atmospheric metacentre, is:
V
Author - Vladimir Sukhanov
Translation - Valentina Sukhanov
Atmospheric cyclones and anticyclones, and also concentric atmospheric turbulences present large obstacles for safe flights. In those cases flying apparatus can get large lateral overload (accelerations), which can throw down it into "spin".
X'(2X+dX)/(X+dX)+ (X+dX/2)+X"[X'/(X+dX)+(2X+dX)dX/X'(X+dX)],
- angular velocity of rotating cyclone or anticyclone;
= ' - angular acceleration of the rotation of the atmospheric section;
X'(2X+dX)/(X+dX)+(X+dX/2)+X"X'/(X+dX)+X"(2X+dX)dX/X'(X+dX) .
1)
X'(2X+dX) / (X+dX)
2)
(X+dX/2)
3)
(X+dX)
4)
X"(2X+dX)dX / X'(X+dX)
of the concentric motion has tendency to decrease to zero. In this case acceleration can arise not less strong and risk than from the acceleration 1). This means that flight apparatus should not change its linear speed (should not allow linear acceleration X ") during crossing of the section of the atmosphere with the concentric motion, whose circulation has tendency to slowing down.
X'(2X+dX) / (X+dX)+ (X+dX/2)+X"[X ' /(X+dX)+(2X+dX)dX / X'(X+dX) ],
(see symbols meanings in supplement 2.1)
It is published in the bulletin VNTIC "Ideas. Hypothesises. Solutions" N 2, 2002 years.
Copyright - Vladimir Sukhanov 2001, 2002, 2003
Concealed Force
- X' - linear relative velocity of an object when the vector of its motion crosses centre of rotation of the frame of reference
- - angular velocity of rotation of frame of reference,
X'
But if we take
- Ex = M(X')2 / 2 - kinetic energy of rectilinear relative motion of an object
- Ev = Mv2 / 2 - kinetic energy of motion of the object in a circle
- E = M X"cX - work which is made by centrifugal and centripetal forces, when of the object displaces
- Ek = M X"l - work which is made by Coriolis' force (arising as a result of Coriolis' acceleration) when the object displaces
- M - mass of the object
- V - speed of the object motion in a circle
- X"c - centrifugal (centripetal) acceleration
- I - displacement of the object in a circle and the equation of Energy Conservation Law takes next view for that case
+ Ek = const,X'(2 X + d X)/(X + d X)
- X - a distance from the object to the frame of reference
- dX - an increasing of X
1. Book "Inventive Creation" in Russian in 2003, ISBN: 5-94990-002-2.
2. Magazine "New Energy Technologies" No 5-6, 2003. ISSN 1684-7288.
3. Patents of the USA http://www.rexresearch.com/intertial/intrtial.htm