An Alternative Form of Euler’s Equation for the Rotational Dynamics of a Rigid Body Confined to Planar (2-D) Motion

This paper explains why Euler's equation and the airfoil theory, while analytically correct, sometimes produce disappointing results. It also emphasizes the merits of a recently developed approach and demonstrates its usefulness in solving problems encountered in practice. The subject matter relates, directly, only to rotodynamic pumps. However, with proper modifications, it can be easily expanded to other fluids machines.

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A Correlation between Aerofoil Theory and Euler's Equation for Calculating the Head of a Constant-Pitch Axial-Flow Inducer

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1243/pime_proc_1987_201_135_02 ◽

1987 ◽

Vol 201 (5) ◽

pp. 357-363 ◽

Cited By ~ 2

Author(s):

S Yedidiah

Keyword(s):

Axial Flow ◽

Impeller Blade ◽

Euler’S Equation ◽

Constant Pitch ◽

Euler's Equation

This study indicates that the aerofoil theory of an impeller blade is not interchangeable with Euler's equation. Instead, these two approaches are supplementary to each other. The conclusion is well supported by observations from practice.

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On Darboux solutions of the Euler's equation

Aequationes Mathematicae ◽

10.1007/bf01836450 ◽

1989 ◽

Vol 37 (2-3) ◽

pp. 279-281

Author(s):

J. Smítal

Keyword(s):

Euler’S Equation ◽

Euler's Equation

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A unified approach to rigid body rotational dynamics and control

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2011.0233 ◽

2011 ◽

Vol 468 (2138) ◽

pp. 395-414 ◽

Cited By ~ 16

Author(s):

Firdaus E. Udwadia ◽

Aaron D. Schutte

Keyword(s):

Rigid Body ◽

Closed Form ◽

Equations Of Motion ◽

Fundamental Equation ◽

Rotational Dynamics ◽

Constrained Motion ◽

Dynamics And Control ◽

Common Framework ◽

The Stability ◽

And Control

This paper develops a unified methodology for obtaining both the general equations of motion describing the rotational dynamics of a rigid body using quaternions as well as its control. This is achieved in a simple systematic manner using the so-called fundamental equation of constrained motion that permits both the dynamics and the control to be placed within a common framework. It is shown that a first application of this equation yields, in closed form, the equations of rotational dynamics, whereas a second application of the self-same equation yields two new methods for explicitly determining, in closed form, the nonlinear control torque needed to change the orientation of a rigid body. The stability of the controllers developed is analysed, and numerical examples showing the ease and efficacy of the unified methodology are provided.

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Editorial-The Proof of Euler's Equation

American Mathematical Monthly ◽

10.2307/2305744 ◽

1948 ◽

Vol 55 (2) ◽

pp. 94 ◽

Cited By ~ 1

Author(s):

C. B. Allendoerfer

Keyword(s):

Euler’S Equation ◽

Euler's Equation

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