First, let us clarify that the term “reciprocating-rotational motion” here will be called movements similar to the movement of pendulums.
Consider the behaviour of a physical pendulum, performing a reciprocating-rotational motion with a span of 180 degrees.
Reciprocating-rotational motion has unique properties.
The body making a reciprocating rotational movement changes the direction of movement at the extreme points of its trajectory. At the same time, if the rotation of the body is limited to 180 degrees, then immediately before the passage of both extreme points, the direction of movement of the body relative to space is identical. Accordingly, in the first moment after passing the extreme points, the direction of motion of the body relative to space is also identical.
Consequently, the system of two bodies performing anti-phase reciprocating rotational motion does not change the direction of its linear acceleration in space during the entire cycle of motion. At the same time, the centrifugal accelerations of this system also do not change their direction in space during the entire cycle of motion. But the directions in the space of linear and centrifugal accelerations are mutually opposite.
These properties of the system of two pendulums allow to create on its basis “reactionless” thrusters.
The term reactionless is not the most appropriate, but it has already come into usage and therefore we have to use it, prefacing by the necessary explanations: “reactionless” drives actually have a support (reaction), and this support is the ether. The best definition is a more detailed one: “propulsors without jet mass ejection”, therefore further in the text under the term “reactionless” we will mean the propulsor without jet mass ejection.
“Legalization” of the reactionless movement is a long-overdue necessity. Inventors of functioning reactionless devices have to justify violations of the laws of Newton, devising “evidences” of the conformity of their inventions to these laws. This is a completely absurd situation, as Newton’s laws distort the real picture of the world and are an obstacle to technological progress.
It is time for the enthusiasts of the reactionless (support-less) motion to stop feeling like outcasts, and finally gain confidence in their rightness. The Law of Mechanics serves them in this task as the support (intentional pun), as a powerful tool for investigation of the physics of reactionless motion. Functioning reactionless devices are a convincing confirmation of the validity of the Law of Mechanics, and in turn, the Law of Mechanics allows the creation of such devices.
When creating reactionless devices using centrifugal forces, the primary task is to obtain unidirectional linear acceleration.
Simple (unidirectional) rotation inevitably causes an omnidirectional centrifugal acceleration, of which it is necessary to separate a unidirectional linear acceleration and to compensate for the opposite direction. Such compensation complicates the system, and reduces the efficiency of the drive, as it is a partial compensation that does not eliminate completely negative acceleration.
Unlike a simple unidirectional rotation, the rotation with a cyclic change of direction, which is the characteristic of the pendulum, allows one to completely avoid the formation of reverse linear accelerations.
Consider the behaviour of the body performing a cyclic reciprocating motion (180 degrees rotations) under the action of some internal force (for example, a spiral spring).
The first part is the analysis without centrifugal accelerations.
Figure 1 shows the position of the pendulum load at the beginning of the cycle in the direction of the black arrow. In this position, the speed of the load “V” is minimal and the acceleration “a” is maximal. In accordance with the Law of Mechanics, the load will experience the force “F” applied to it from the ether and directed opposite to acceleration.
This is the force of inertia, and it occurs due to the acceleration of the ether relative to the load. The ether is stationary, and the acceleration of the load relative to the ether is equivalent to the acceleration of the ether inside the load in the opposite direction.
With the accelerated movement of the load in the first sector, an external force will be applied to the entire system, moving the entire drive in the opposite direction.
Figure 2 shows the position of the load in the middle between the first and second cycles. In this position, the speed of the load “V” is at maximum, and the acceleration “a” is zero; since at this point the acceleration changes its direction, and then begins to act in the opposite direction, slowing down the load. Accordingly, the force from the ether caused by the linear acceleration of the load at this point will be absent (zero).
In fact, the force applied by the ether at this point still exists, it is a centrifugal force, but in this part of our analysis, we do not consider it yet, since now we are interested in the acceleration resulting from the “simple” linear motion of the load.
And the purpose of this limited analysis is to show that rotational motion provides a smooth change in the direction of linear motion of the body to the opposite direction, without intermediate stop of the body.
Such a stop is inevitable in the case of reciprocating motion. But in the case of reciprocating-rotational motion, the change of direction occurs without linear acceleration.
Stops and subsequent linear accelerations occur at the beginning of phase 1, and at the end of phase 2, and at both of these points accelerations have the same direction with respect to the surrounding space. As a result, the load acquires unidirectional accelerations, i.e. it can move pushing off from space.
In fact, the system will move in the opposite direction, and we will discuss this fact later, but for now we will continue to consider the process of reciprocating-rotational motion.
Figure 3 shows the position of the load at the end of the driving cycle. In this position, the load speed “V” is reduced to a minimum and the braking (negative acceleration) “a” is maximum. In accordance with the Law of Mechanics, the load will experience the force “F” applied to it from the ether and directed in the opposite to direction of acceleration, that is, in the same direction as before (in position 1).
As we can see, an external force applied from the ether accompanies the reciprocating-rotational movement of the load. This force has the same direction in the mirror-symmetrical points of the trajectory of the load, that is, the load does not change the direction of its acceleration relative to the ether. This is due to the fact that the load changes the direction of speed and at the same time the sign of acceleration changes (i.e. acceleration is replaced by braking).
After that, all the processes are repeated in the opposite direction. And again there is an inversion of the acceleration of the load in the second half of the cycle, as the direction of movement of the load changes due to its rotation.
Below are the graphs of the load speed “V” and the projection of linear acceleration on the horizontal coordinate axis. The velocity is a monotonically increasing (the acceleration “a” = const) to a maximum at the point of 90 degrees, and then decreases to zero at point 180 degrees.
The scale of linear acceleration on the chart is enlarged by 10 times, otherwise the acceleration chart will be almost indistinguishable from a straight line.
The following graph is supplemented by centrifugal acceleration.
Finally, the sum of linear and centrifugal accelerations
As can be seen from the last graph – linear acceleration does not play a significant role in the total acceleration, since the centrifugal acceleration is in the quadratic dependence upon the linear velocity.
But it is noteworthy here that the linear acceleration is perfectly symmetrical with respect to the axis passing through 90 degrees.
Therefore, in the total acceleration of a system consisting of two coaxial or symmetrical antiphase pendulums, there are no components causing lateral displacements. That is, despite the rotational nature of the movement of loads, the resulting force is linear, unidirectional.
Now on the dependence of the resulting accelerations of the system on the linear accelerations of the weights that generate them. Take the radius of rotation of the load equal to one unit, the mass of each load one unit, and the total mass of the system consisting of two loads and the surrounding mechanisms and payload for 16 units (that is, the total mass of the system is 8 times more than the mass of weights). The full cycle of movement of weights (acceleration plus braking) will take equal to 35 seconds. Then the acceleration of weights equal to 0.01 units of length per second squared, will cause ten times greater acceleration of the system at the time of passage of load through the axis of symmetry (90 degrees). Acceleration of load equal to 0.1 units, will lead to a hundredfold acceleration of the system. A acceleration of load equal to 1 unit, will cause a thousandfold acceleration of the system.
Finishing with the first part of the section devoted to the reciprocating-rotational motion, we note that the priority for the reciprocating-rotational engine “Inertor” belongs to E. I. Linevich, who presented the geometric justification for its work based on Newton’s laws.
“Inertor” differs from invented in the 1930s by V. N. Tolchin mechanism “Inertoid”, which used unidirectional rotary motion with variable angular velocity. As we have already noted — unidirectional rotation leads to the appearance of oppositely directed accelerations, which have to be compensated.
The Law of Mechanics 