Andrew Charniga
www.sportivnypress.com
“If you want to find the secrets of the universe, think in terms of energy, frequency and vibration.”
Various essays have dealt with a weightlifter’s supra – strength potential to produce energy from the body’s bio – spring system (tendons, ligaments, fascia) {Charniga, www.sportivnypress.com}. The release of elastic energy from the rapid stretching and recoil of the body’s main bio – spring, the Achilles tendon, is a critical component of the weightlifter’s; or for that matter, any athlete in power sports; an innate ability to produce and release energy greater and faster than is possible from muscle contraction alone (Biewener, 2015, Roberts, 2011).
However, there is little in the weightlifting literature about the skillful use of elastic recoil of the barbell, i.e., an external addendum; and, almost nothing on how the oscillation of the barbell can impact a weightlifter’s coordination during performance of the classic exercises.
Furthermore, there is little if anything in the literature concerning the affect of barbell oscillation/vibration on the weightlifter’s physiology; likewise, the skill to coordinate release of elastic energies from the barbell’s elastic recoil with those energies from the weightlifter’s bio – springs. The effects of barbell vibration/oscillation and deflection (bend) on weightlifting technique involves physics, physiology and the weightlifter’s skill to coordinate the two: the physics with physiology.
Variations in barbell deflection & bending within a bend
Medvedyev, et al, 1990 measured barbell deflection (bend) from the center of the bar to end of the sleeve, at the bordering instants of 2nd & 3rd phases, in the 3rd phase, the bordering instants of 3rd and 4th, 4th and 5th and in the 4th phases of the pull to determine the degree and variation of bar deflection in the clean. The authors concluded many lifters do not realize maximum the recoil energy of the barbell. Elite lifters made better use of this ‘external adendum’ of energy to lift the barbell than lower qualified lifters.
However, it was noted, a “pre – mature rise onto the toes with flexing of the arms caused another bend in the bar as the lifter was executing the final straightening of the legs in the pull.
Why this heel raise is considered “pre – mature”; and, as such, would be considered a mistake was not explained. One is left to wonder what effect, if any, the ‘extra’ bend, and the addendum energy resulting from the heel raise facilitated the lifter’s technique? A valid question considering the ‘pre – mature’ heel raise is reactive; not a mind to muscle action of volition.
Figure 1. A further bowing of the barbell in the explosion phase of the pull can occur when the lifter rises onto the toes before the knees have stopped straightening. Coincidence? The spring in the arch of the foot (the plantar fascia) is pulled taut as the heels raise and the bar bends. It is possible a ‘pre – mature’ heel raise is a reaction to coordinate the physiology, i.e., a release of additional elastic energy from the foot with the release of strain energy from the bowing steel ( the physics). Charniga photo.
An example of a bending – within – a – bending is the assumed premature bending of the arms in the pull phases of the classic exercises. According to the classic Soviet model and still considered valid today; for the most part, the arms are to remain straight throughout the pull phases until the lifter has fully straightened the legs and trunk. Flexing the arms before the aforesaid straightening of legs and trunk is believed to reduce the force against the support; dampening the output of the muscles straightening the legs and trunk (see figures 2 & 3).
Figures 2 & 3. Two examples of bar bend in the pull phases of the clean. On the right in figure 2 the lifter’s arms have remained straight whereas the lifter on the left has flexed her elbows; generally considered and error in technique. Both barbells are relatively straight in figure 2. In figure 3, the barbell of the lifter on the right has bowed slightly as her arms have remained straight; whereas the lifter on the left has allowed her arms to straighten which resulted in a visibly greater bowing of ‘her’ barbell. Charniga photos.
The lifter on the right will receive the benefit of a recoiling barbell as she fully straightens her legs and trunk; whereas, the recoil energies from the lifter on the left are presumed dissipated in the arms (figure 2).
However, from a different a vantage point, i.e., a parallax view if you will; the production and transfer of energy in the pull; the next set of figures (figure 3) would indicate the strain energy of the lifter with bent arms has shifted into bending her barbell, i.e., kinetic energy converted to potential. The potential energy of both the bowing barbells will be released in the form of an elastic recoil; which in turn will ‘lessen’ the weight of the barbell.
However, the recoil of the bending barbell of the woman on the left, has been ‘delayed’ to later on in the exercise; whereas the barbell of the lifter on the right has already straightened (recoiled) earlier in the exercise (see figure 3).
The arms of the lifter on the left have straightened and the barbell has bowed, i.e., the strain energy of the arms has been transferred to the barbell. From here, what would be considered ‘lost’ energy from a premature bending of the arms hasn’t been dissipated; it has been shifted to be released in a forthcoming elastic recoil of energy from the barbell.
Release of elastic energy and ‘supra strength’
Coordinated release of the collective energies from the oscillation/deflection of barbell with the elastic recoil of the weightlifter’s bio – springs (tendons, ligaments and fascia) are the principle source of the weightlifter’s supra strength, i.e., the possibility to release more energy, faster than is possible from muscular contraction alone.
Consequently, old ideas with respect to pre – maturely raising the heels, flexing arms, shoulders behind the the vertical projection of the bar, hips rising faster than shoulders in the pull and so forth; however, logical, should be re – assessed from the standpoint of the weightlifter’s effectiveness in producing and releasing elastic energy to successfully lift a barbell.
It is in this context, weightlifting technique should be defined in terms of the weightlifter’s ability to release elastic energy from muscles, tendons, ligaments, fascia and the coordination of the aforesaid with the elastic deformation of the barbell. Hence, a weightlifter with optimum technique endeavors to find the most effective movement of energy, i.e., the ‘supra strength’; with significantly less attention devoted to barbell trajectory, barbell speed and so forth.
Forms of bar deflection: classic bend; hyper-bend; oscillation/vibration; horizontal bend
Two forms of classic bend in the barbell are 1/ the bowing of the center of the bar caused by the oscillation of the discs; 2/ the bowing of the center of the bar before the discs separate from the platform. In both cases, the center of the bar and the discs move in opposite directions (or briefly remain on the platform): the center moves up and the discs down; and, even vice versa.
Figure. A classic bend in the bar from the floor. The 25 kg discs separate from the platform first whilst the 15 kg discs separate as bar bend reaches maximum. Charniga photo.
Typically, the heavier the weight, the more abruptly the weightlifter pauses and shifts direction of movement (see figures 4 & 5) the greater the deflection. For instance, maximum bar bend in the clean typically occurs at extreme bottom of the squat when the lifter’s lower extremities reach their geometric limits; that is to say, the legs are unable to flex further when rear of the thigh is flush against the rear of the shank and the shins cease tilting forward (see figure 4).
Figure 4. The relative largest deflection of the barbell in the classic exercises: the discs continue to descend after the lifter has reached the geometric limits of flexion in ankle, knee and hip joints. Charniga photo.
The discs continue to move downward (figure 4) after the lifter has stopped flexing at the bottom of the squat. The lower extremities are unable to flex further due to geometric constraints: the back of the thigh rests on the shank restricting further movement, i.e, the lifter is unable to bend further. The descending discs provide more energy to the already significant energy arising from the abrupt pause at the extreme low point of the squat. Which in turn, increases the already accumulating strain energy in the tendons, ligaments and fascia from the rapid descent of the lifter – barbell unit.
Skillfully coordinating the barbell’s elastic recoil with the release of strain energy from bio – springs (tendons, ligaments, fascia), will reduce significantly the work required of the lower extremity musculature to stand from the low squat. In effect, this coordination of elastic recoil of metal with the release of energy from Biological springs is a prime example of producing ‘supra energy’, a coupling of Physics with Physiology (figure 4).
The production of ‘supra energy’ arising from the coordination of elastic recoil of energy from the bowing barbell with that emanating from stretching tendons and ligaments as well as muscles, i.e., the coordination of Physics with Physiology; reduces significantly, the force of muscle contraction alone required to stand from the low squat. Effective coordination of Physics with Physiology diminishes the significance of large volumes of squatting heavy weights in training; so as to be able to stand from the deep squat.
Combining the Physics with the Physiology enables the weightlifter to coordinate the collective energies of elastic deformation of steel with that released from the bio – springs. That is say, one does not endeavor to “catch the bounce” at the bottom of the squat, as is the common refrain. “Catching the bounce” denigrates the concept of skill; to a happenstance. In actuality, the coordination of muscular effort, the timing of barbell recoil (the Physics) with the elastic recoiling of tendons, ligaments and fascia (the Physiology) is a skill; not a haphazard event.
A bend within a bend in the jerk from the chest
Maximum bar bend in the jerk from the chest typically occurs when the lifter abruptly stops bending knee, hip and ankle joints at the extreme low position of the half – squat {Zkekov, 1976} (see figure 5).
Figure 5. Maximum bend in the jerk typically occurs at the bottom of the half – squat when the lifter switches from bending the knees to straightening. However, top lifters can continue to bend the bar as they straighten the legs, i.e, the discs continue to descend as the lifter’s legs are straightening. Charniga photo.
However, later research (Ivanov and Roman, 1981; Medvedyev, et al, 1981) showed that the switch from bending to straightening at the lowest point of the half squat for the jerk can be so brief; a further bending, i.e., a ‘bend within a bending’ barbell can be produced by elite lifters. That is to say, top lifters are able to reverse direction from bending to straightening the legs in the half squat of the jerk so fast; so as to be straightening the legs as the discs continue moving down, i.e., further deflecting the barbell after bar bend, presumably would have expected to stop at the bottom of the half squat.
So, an ‘addendum’ deflection of an already bending barbell, can occur when the bar continues to bend after the lifter switches from bending to straightening the legs during recovery from the half squat. In this instance, the lifter bends the bar further as he/she rises from the bottom of the half squat; while straightening the legs; as opposed to reaching maximum bend in the bar from stopping at the bottom of the half squat; then reversing direction.
This is another example of a weightlifter’s potential to express ‘supra – strength’. A ‘bend within a bend’ of the barbell can release additional strain energy than otherwise would seem possible; with the additional opportunity to combine the elastic recoil of the steel (the Physics) with that of the lifter’s tendons, ligaments and fascia; which are arranged in series from foot to hip (the Physiology). The coupling of the physics and physiology produces the conditions for release of more energy, faster, than would otherwise be possible from contraction of lower extremities musculature alone (see figure 5). The half – squat/thrust phase of the jerk is generally perceived to be a function of the power of muscle contraction to drive the barbell vertically. However, it can, and should be much more. Some estimates (Vorobeyev, 1977) figure up to 50% of the weight of the barbell can be ‘freed up’ under optimal conditions in the half – squat thrust phase of the jerk from the chest.
I.P. Zhekov (1976) observed this ‘bend within a bend’ phenomena in his analysis of the jerk. However, he hypothesized this instantaneous reversing of direction from bending to straightening was too difficult for the lifter’s muscles to cope. Consequently, he felt a slight pause at the bottom of the half squat was more appropriate.
Nonetheless, if one characterizes this action of straightening the legs as the discs continue to move downward, as an elastic recoil of tendon, ligaments, and fascia to produce a further bend in the already bending elastic steel, i.e., springs acting against another springy material; it sidesteps the issue of this bending of the bar, as the legs begin straightening; as being too much for the muscles.
‘Hyper – bend’
Another form of barbell deflection is a ‘hyper – bend’. A ‘hyper – bend’ occurs when the center of the bar is bowed by the lifter flexing the lower extremities. The center of the bar bows down as the discs move up.
The speed with which the weightlifter switches direction is the main means of achieving a hyper-bend; an especially fast descent under the barbell in the classic snatch, the classic clean and the classic jerk can produce a ‘hyper bending’ of the bar. The lifter’s speed of descent, by its very nature must exceed the speed of a free falling body, or 9.8 m/sec². Such abrupt and rapid reversals of direction during the descent phases of the classic exercises can produce a ‘hyper – bend’ where the center of the bar and the discs move opposite (see figure 6).
Figure 6. The lifter’s high speed descent into the squat creates a ‘hyper – bend’, i.e., the center of the bar is bowed down relative to the rising discs; in line with the athlete’s movement down. Charniga photo.
A ‘hyper – bend is another opportunity to take advantage of the physics of weightlifting to produce ‘supra – energy’. A rapid descent into the squat and equally rapid reversal of directions allows the lifter take advantage of the extra distance the discs move to straighten the bar from a hyper bend; before continuing downward, until a maximum deflection in the barbell occurs. An elite lifter’s rapid movements can couple the extra energy of the physics (bending steel) to the physiology of the elastic recoil properties of the bio-springs; to release substantially more energy, and release it faster than is possible with muscle contraction alone.
All other things being equal, the faster the weightlifter’s movements the more the barbell will potentially bend; hyper – bend and classic bend combined; the more potential energy is produced in the bending steel as well as the forthcoming stretching of the bio-springs; the more energy produced from the combined recoil of steel and elastic tissues.
Bar bend at the start of the jerk
Barbell bend varies in the starting position of the jerk from the chest. A bow in the barbell at the start means the barbell has to first straighten as the half squat begins. This straightening out of the barbell as the lifter bends in the half squat is another possible addendum of elastic energy potential which can increase deflection of the barbell when the athlete recovers from the half squat (see figure 7).
Furthermore, there is some relaxation, a lessening of tension of lifter’s muscles; as the bar straightens; a physiological consequence to the straightening steel. As the lifter bends the knees during the half squat; the discs rise as the center of the bar straightens. Consequently, the force of the barbell’s weight acting on the athlete is 30 – 50% of the barbell’s actual weight (Zhekov, I.P., 1969); even though the weight is resting on the lifter’s chest. This circumstance is a little known factor of the variable weight of the barbell pressing against the weightlifter’s body; even as it is being supported (figure 7).
Figure 7. A lifter in the static posture for the jerk from the chest (upper photo) and the beginning of the half – squat (lower photo). The barbell is bowed in the top photo. As she begins the half squat for the jerk the barbell straightens as the center of the bar moves down (lower photo); the discs move opposite the center of the bar. This in turn creates of an optical illusion of the discs rising as the lifter’s knees begin bending. Charniga photos.
By the way, all of this, in its turn, is a factor for determining the width of the grasp in the jerk. Barbell deflection can be greater with a shoulder width or close to shoulder width hand spacing (I.P. Zhekov, 1976). The wider the hand spacing relative to shoulder width, the greater the likelihood the hands can ‘support’ the bar such that it will tend to bend less (I.P. Zhekov, 1972):
“The hands should be positioned as close as possible to create favorable conditions for oscillating the discs.” I.P. Zhekov, 1972
Knowledge and expertise in the training and competition performance of today’s weightlifters is decidedly moving in the wrong direction. Hence, a shoulder width hand spacing for the jerk can be viewed as a negative. This of course means the opposite is true. A wide hand spacing as it is commonly practiced, is a futile effort to ‘hide’ from gravity. That is to say, it is incorrect to assume a wider hand spacing means the lifter has less distance to lift the barbell, and, as result it will be easier to lift it to outstretched arms overhead.
The fact of the matter is, the negatives of such an idea outweigh any conceivable advantage. There is typically less bend in the barbell with a wide hand spacing (Zhekov, 1972). Furthermore, the poor muscle leverage of a wide had spacing (Vorobeyev, 1988) increases the difficulty for the lifter to fix and hold the barbell on outstretched arms. Consequently, the potential to realize ‘supra -strength’ with a wide hand spacing is less than with a shoulder width hand spacing, i.e., widening the grip makes it harder to jerk it; not easier.
The effect of the disposition of the feet on the elastic potential in the clean and jerk
A starting position with the feet arranged at approximately pelvis width is the generally accepted rule of thumb; optimum stance, for the jerk from the chest. Logic dictates spacing the feet wider; even to shoulder width; would tend to reduce the potential bar bend from the half – squat/thrust phases of the jerk. The reason being the disposition of the feet (the support) would be further outside the vertical projection of the center of the bar.
However, positioning the feet inside pelvis width would tend to produce more bar bend as the support (the feet) are close to the center of the bar; all the more so, when the hands are grasping the barbell close to shoulder width (see figure 7). Furthermore, there would tend to be more bend in the ankle joints; a greater involvement of the calf muscles and especially more stretching of the Achilles tendon producing greater potential elastic recoil. (see figure 7).
Figure 7. A world record in the clean and jerk with an inside pelvis width stance and a ‘normal’ shoulder width grasp of the barbell. This stance would logically tend to produce more elastic deformation of the barbell because the feet are arranged closer to the vertical projection of the center of the barbell; and, likewise more integration of ankle muscles and tendons. Charniga photo.
A disposition of the feet inside the vertical projection of the shoulder joints should be a considered to produce more barbell deflection. However, it is not a guarantee of a successful jerk. For one thing, the lifter would want to make sure ankle mobility would accommodate the narrow foot spacing in order to yield the desired result.
Horizontal deflection: barbell bending away from body center of mass
Figure 8. Example of a significant horizontal barbell deflection as the bar contacts the lifter’s pelvis. Charniga photo.
For the most part, barbell bend, as well as oscillation/vibration is assumed to occur exclusively in the vertical plane; because a lifter is generating power vertically to raise the weight, i.e., pressing down with the feet to produce a vertical lift. However, the forces on the barbell are never strictly vertical. Indeed, an elite lifter produces a horizontal displacement of the barbell towards the body from the instant of barbell separation from the platform; due to a forceful horizontal effort against the support: the effect is both vertical and horizontal.
That being said, a horizontal shifting of the barbell towards the lifter as the knees and trunk straighten can bend the barbell towards the lifter’s body; which is obvious from figure 8. The question arises as to whether a significant horizontal bend as depicted in figure8; constitutes wasted energy, i.e., the energy from the recoil of the barbell will be in the opposite direction; away from the athlete; increasing the moment force of gravity on the lifter’s muscles.There is little if any research to support this one way or another. However, it is safe to say the female (15kg) bar will deflect horizontally more than the 20 kg male bar. So, the conundrum remains; as to the negative consequences of the too flexible 15 kg barbell and its potential for negative impact on the female weightlifter.
The Physics of vibration/oscillation effect on Physiology: Kinesthetic illusions
Oscillation/vibration as referenced here denote relatively small fluctuations in discs of varying rhythm and speed.
Figure 9. A lifter’s elbows unlock after first reaching full extension. Conceivably this circumstance may be caused by kinesthetic illusions, i.e., a reflex contraction of arm flexor muscles induced by the barbell oscillation. Charniga photo.
A ‘known known’ of weightlifting is the fact oscillation of the discs produce fluctuations of greater and lesser tension in the lifter’s muscles (Zhekov, 1972). Increasing tension in the muscles occurs when the discs descend; bowing the barbell downward (figures 4 & 5); and, vice versa, there is less tension in the lifter’s muscles than otherwise would be present when the discs shift upward.
For instance, the relatively large downward bow (the inertia) of the barbell in figure 4 could add an estimated 25% resistance to weight of the barbell. In effect, a barbell of 100 kgs would be roughly equivalent to 125 kgs when the discs bow the bar downward; and, be lighter than 100 kg when the oscillating discs bow the bar upwards (see figure 6). At any rate, these inertia affect the weightlifter’s Bio – spring system.
For instance, potential energy is created when the discs bow the barbell upward (figure 6) which is the then added to the inertia of downward bend in the barbell; when the lifter stops flexing under it (figure 5). The potential to generate supra energy from coordination of the elastic recoil of the barbell with that of the tendons, ligaments and fascia lies in the weightlifter’s skill to utilize all this energy addendum effectively.
A known unknown is more likely a unknown unknown (Donald Rumsfeld) in weightlifting sport; how does barbell oscillation/vibration affect the weightlifter’s physiology. Research has shown vibration of muscles can produce kinesthetic illusions (Latash, Zatsiorsky, 2016). Kinesthetic illusions are perceived sensations of “impossible anatomical joint positions” causing involuntary firing of antagonist muscle groups; loss of balance and other unknown effects (Latash, Zatsiorsky, 2016). For instance, vibration of the barbell at outstretched arms may have negative consequences with respect to kinesthetic illusions. The kinesthetic illusion effect could cause the elbows to unlock from unconscious contraction of the biceps and other arm flexors (see figures 9 & 10).
The fact of the matter is, many lifters have lifts turned down due to some wobble of the elbows, i.e., one or both arms unlock after the lifter has lifted the weight to fully outstretched arms; lends credence to a theory of kinesthetic illusions as to the cause of involuntary, slight bend/wobble in one or both elbows.
Without question, the weightlifter’s muscles are subject to considerable vibration from a combined movement of the body and the resultant vibration/oscillation of the barbell. Even the skeleton will vibrate from walking; with waves propagated throughout the body; affecting the muscles and other soft tissues (Alexander, 1997). Presumably, the forceful re – arrangement of the feet in weightlifting, intensified by the weight of the barbell, would logically be expected to cause significantly more oscillation of the skeleton than merely walking. This vibration on top of the oscillation of the barbell.
There is nothing in the weightlifting literature on this subject. These circumstances should be a consideration; such that a revision of the technical rules is in order to eliminate the elbow wobble; incorrectly referred to a “press out” infraction. Lifting the barbell to fully outstretched arms with elbows fixed and remaining immobile 100% of the time; is an impracticality. A small wobble is a natural reaction to the complexity of fixing an oscillating barbell, and, as such is not a sign of imperfection in the lifter’s technique or a strength deficit. This circumstance is all the more pertinent for the female lifter who is forced to control a too flexible 15 kg barbell.
Physics of an oscillating barbell
“The hands should be positioned as close as possible to create favorable conditions for oscillating the discs.” I.P. Zhekov, 1969
There exists little research in the weightlifting literature of the role of barbell vibration. Elastic deformation and recoil of the barbell deals mostly, if not exclusively, with the clean and jerk; due to the width of the hand spacing. The narrower than the snatch, hand spacing, employed in the clean and jerk produces more elastic deformation, i.e., a greater deflection of the bar from its normal straight disposition. Skillful utilization of the elastic recoil from the deflection can assist the lifter to ‘free up’ from the weight of the barbell in order to squat under in both the pull phase and the jerk phases of the lifts quickly; which in its turn permits the lifter to raise bigger weights; especially with less energy from muscular contraction.
Figure 10. However slight, the barbell can flex in the snatch with potential to produce kinesthetic illusions similar to the narrower spacing of the jerk. Charniga photo.
However, it is possible for the bar to oscillate in the snatch if the hands are close enough. This is besides a horizontal bend from contact of the bar on the pelvis or thighs. There is nothing in the literature concerning the effects of either. Nonetheless, the potential of even the slight oscillation of the barbell in the snatch can have negative consequences if the arms involuntarily flex with the weight overhead. The athlete depicted in figure 10 suffered a groin injury struggling to balance 128 in the low squat. Although slight; the bar is visibly bending; the oscillation of which conceivably contributed to the injury as she struggled for equilibrium. This is another concern for consideration to alter the specifications for the 15 kg barbell.
Conclusions
For the most part most coaches and athletes are aware of a classic bending and subsequent recoil (straightening) of the barbell at barbell separation from the platform; and, likewise, the bend and recoil in the jerk from the chest (see figures 5; 11-12). However, there is much more to weightlifting technique than the obvious. Considerably more potential for the weightlifter to produce supra – strength from the skillful combination of elastic recoil of steel and Bio- springs; than such antiquated notions as “catching the bounce” in the clean, and the like.
/ a modern viewpoint of weightlifting strength encompasses the entire spectrum of the weightlifter’s potential to produce and release greater energy and release it faster than is possible from mere mind to muscle contraction. Consequently, a weightlifter’s skill of strength should be defined as the efficient production and shifting of energy; elastic strain energy released from Biological springs, strain energy from an elastic recoil of the barbell synchronized with energy from muscle contraction. Concepts of weightlifting strength being determined primarily by muscle mass, cross fiber areas, short stature advantages, and so forth are antiquated.
Figure 11-12. Weightlifters create a noticeable bowing of the barbell {deflection} from the platform; subsequently, the bar straightens as the lifter stands from a crouched posture and the ‘discs catch up’. The speed with which the lifter switches from lifting up to dropping down, referred to as “the freeing up” will decide how well the energy released from elastic recoil is utilized. Charniga photos
References
/ Medvedyev, A.S., Lukashev, A.A., Kanyevsky, V.B., Ismailov, I.S., Peculiarities of the elastic deformation of the bar during the clean”, Teoriya i Praktika Fizicheskoi Kultury, 5:43-46:90; Weightlifting Technique and Training, Sportivnypress.com, Livonia, Michigan. Translated by Andrew Charniga
/ Zhekov, I.P., Biomechanics of the weightlifting exercises, English translation: Weightlifting Technique and Training, Sportivnypress.com, Livonia, Michigan. Translated by Andrew Charniga
/ Zhekov, I.P. “Utilizing the Elastic Qualities of the Bar in the Weightlifting Exercises”.Tribuna Masterov, FiS, Moscow, 66 – 71:1969. Translated by Andrew Charniga
/ Zhekov, I.P., Tiiazhelaya Atletika. Uchebnik dla In – tov Fizicheskoi Kult. Editor A. N. Vorobyev, PP 64 -65:1972. Translated by Andrew Charniga
/ Medvedyev, A.S., Masalgin, N.A., Frolov, V.I., A.G. Herrera, A.G., “The Interconnection Between the Parameters of the Jerk” Teoriya I Praktika Fizicheskoi Kultury, 6:6-7:1981. Translated by Andrew Charniga
/ Astrand, P- A., RoDAhl, K., Dahl, D., Stromme, S., TEXTBOOK OF Work Physiology, 2003; Human Kinetics