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Water entry of a body which moves in more than six degrees of freedom.

ABSTRACT: The water entry of a three-dimensional smooth body into initially calm water is examined. The body can move freely in its 6 d.f. and may also change its shape over time. During the early stage of penetration, the shape of the body is approximated by a surface of double curvature and the radii of curvature may vary over time. Hydrodynamic loads are calculated by the Wagner theory. It is shown that the water entry problem with arbitrary kinematics of the body motion, can be reduced to the vertical entry problem with a modified vertical displacement of the body and an elliptic region of contact between the liquid and the body surface. Low pressure occurrence is determined; this occurrence can precede the appearance of cavitation effects. Hydrodynamic forces are analysed for a rigid ellipsoid entering the water with 3 d.f. Experimental results with an oblique impact of elliptic paraboloid confirm the theoretical findings. The theoretical developments are detailed in this paper, while an application of the model is described in electronic supplementary materials.

SUBMITTER: Scolan YM

PROVIDER: S-EPMC4985040 | biostudies-literature | 2015 May

REPOSITORIES: biostudies-literature

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Water entry of a body which moves in more than six degrees of freedom.

Scolan Y-M YM Korobkin A A AA

Proceedings. Mathematical, physical, and engineering sciences 20150501 2177

The water entry of a three-dimensional smooth body into initially calm water is examined. The body can move freely in its 6 d.f. and may also change its shape over time. During the early stage of penetration, the shape of the body is approximated by a surface of double curvature and the radii of curvature may vary over time. Hydrodynamic loads are calculated by the Wagner theory. It is shown that the water entry problem with arbitrary kinematics of the body motion, can be reduced to the vertical ...[more]

PMID: 27547102

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Project description:BackgroundThe etiology of adjacent-segment disease following cervical spine arthrodesis remains controversial. The objective of the current study was to evaluate cervical intervertebral range of motion during dynamic flexion-extension in patients who had undergone a single-level arthrodesis and in asymptomatic control subjects.MethodsTen patients who had undergone a single-level (C5/C6) anterior arthrodesis and twenty asymptomatic control subjects performed continuous full range-of-motion flexion-extension while biplane radiographs were collected at thirty images per second. A previously validated tracking process determined three-dimensional vertebral position on each pair of radiographs with submillimeter accuracy. Six-degrees-of-freedom kinematics between adjacent vertebrae were calculated throughout the entire flexion-extension movement cycle over multiple trials for each participant. Cervical kinematics were also calculated from images collected during static full flexion and static full extension.ResultsThe C4/C5 motion segment moved through a larger extension range of motion and a smaller flexion range of motion in the subjects with the arthrodesis than in the controls. The extension difference between the arthrodesis and control groups was 3.8° (95% CI [confidence interval], 0.9° to 6.6°; p = 0.011) and the flexion difference was -2.9° (95% CI, -5.3° to -0.5°; p = 0.019). Adjacent-segment posterior translation was greater in the arthrodesis group than in the controls, with a C4/C5 difference of 0.8 mm (95% CI, 0.0 to 1.6 mm) and a C6/C7 difference of 0.4 mm (95% CI, 0.0 to 0.8 mm; p = 0.016). Translation range of motion and rotation range of motion were consistently larger when measured on images collected during dynamic functional movement as opposed to images collected at static full flexion or full extension. The upper 95% CI limit for anterior-posterior translation range of motion was 3.45 mm at C3/C4 and C4/C5, but only 2.3 mm at C6/C7.ConclusionsC5/C6 arthrodesis does not affect the total range of motion in adjacent vertebral segments, but it does alter the distribution of adjacent-segment motion toward more extension and less flexion superior to the arthrodesis and more posterior translation superior and inferior to the arthrodesis during in vivo functional loading. Range of motion measured from static full-flexion and full-extension images underestimates dynamic range of motion. Clinical evaluation of excessive anterior-posterior translation should take into account the cervical vertebral level.

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Water entry of a body which moves in more than six degrees of freedom.

Publications

Water entry of a body which moves in more than six degrees of freedom.

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