John H. Heinbockel

Old Dominion University

Department of Mathematics and Statistics

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Nozzle Flow with Vibrational Nonequilibrium

by

John G. Landry

Graduate Student, Old Dominion University, Norfolk, Virginia.

John H. Heinbockel

Professor, Old Dominion University, Norfolk, Virginia.

Willard E. Meador

Senior Scientist, NASA Langley Research Center, Hampton, Virginia.

  • Abstract


  • Nozzle Flow with Vibrational Nonequilibrium

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    Introduction to Tensor Calculus and Continuum Mechanics

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    TROCHOIDS

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    A trochoid is obtained by following a point on the spoke of a wheel as the wheel rolls in a straight line without slipping .

    Consider a circle of radius R as it rolls in a straight line. Tracing the point A , which is a distance less than R along the spoke, produces a curtate cycloid.

    Tracing the point B, which is exactly a distance R along the spoke, produces a cycloid.

    Tracing the point C, which is a distance greater than R along the spoke, produces a prolate cycloid.

    HYPOCYCLOIDS

    Following the motion of a point P on a spoke of a circle of radius b, as it rolls without slipping on the inside of a second circle of radius a>b, produces a curve which is called a hypocycloid.

    • EPICYCLOIDS

    Following the motion of a point P on a spoke of a circle of radius b, as it rolls without slipping on the outside of a second circle of radius a>b, produces a curve which is called a epicycloid.

    Gear teeth are frequently made to conform to the cycloid shape so that there is more of a rolling rather than sliding contact when the gears mesh.

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