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Newton's use of the calculus in the Principia is illustrated by proposition 11 of Book I: if the orbit of a particle moving under a centripetal force is an ellipse with the centre of force at one focus, then the force is inversely proportional to the square of the distance from the centre.
The outcome measure for postural control is the total path of the centre of force over the entire trial.
The primary outcome measure is the change in the subscale bodily pain of the SF36 from M1 to M2. Secondary outcomes comprise the WOMAC score, SF36, isometric strength of hip muscles, spatial-temporal and discrete measures derived from clinical gait analysis, and the length of the centre of force path in different standing tasks.
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The investigation reveals that the centre of forcing has significant effect on the dynamic response of the periodically forced fermentors.
Chaotic behavior is developed when the centre of forcing is relatively close to a homoclinic infinite period orbit, while quasi-periodicity is developed when the centre of forcing is in the neighborhood of a Hopf bifurcation point.
It is shown that period doubling and chaos occur for very small amplitudes of forcing when the centre of forcing is close to the homoclinical orbit.
The investigation concentrates on the less studied case when the centre of forcing is close to the homoclinical orbit of the autonomous system and preliminary results for the effect of the distance between the centre of forcing and the homoclinical orbit are presented.
Corresponding terms for describing the most distant orbital point of bodies moving around centres of force other than the sun include apogee, apocentre, and aposaturnium.
In his philosophy of matter atoms became mere points (albeit possessing mass) acting as centres of force, the forces varying with the distance from the centre and oscillating between repulsive and attractive several times before becoming the inverse square law of gravitation at sensible distances.
After striking the centre of the force plate with left foot, the right foot reached the goal mark.
After striking the centre of the force plate with one foot, the participant cut in a direction 60° lateral to the strike foot, relative to the direction of movement; the other foot then reached the goal mark (Fig. 1).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com