A Method of Deriving Euler's Equation in the Calculus of Variations

1908 ◽  
Vol 15 (3) ◽  
pp. 47
Author(s):  
Gilbert Ames Bliss
Keyword(s):  
Calculus Of Variations ◽  
Euler’S Equation ◽  
Euler's Equation

scholarly journals Hyers-Ulam Stability of Euler’s Equation in the Calculus of Variations

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3320
Author(s):  
Daniela Marian ◽  
Sorina Anamaria Ciplea ◽  
Nicolaie Lungu
Keyword(s):  
Calculus Of Variations ◽  
Direct Method ◽  
Integral Form ◽  
Ulam Stability ◽  
Euler’S Equation ◽  
First Case ◽  
Special Cases ◽  
Euler's Equation ◽  
The Laplace Transform ◽  
First Time

In this paper we study Hyers-Ulam stability of Euler’s equation in the calculus of variations in two special cases: when F=F(x,y′) and when F=F(y,y′). For the first case we use the direct method and for the second case we use the Laplace transform. In the first Theorem and in the first Example the corresponding estimations for Jyx−Jy0x are given. We mention that it is the first time that the problem of Ulam-stability of extremals for functionals represented in integral form is studied.

Euler's Equation and (p, r) Coordinates

1954 ◽  
Vol 38 (325) ◽  
pp. 172
Author(s):  
K. E. Bullen
Keyword(s):  
Euler’S Equation ◽  
Euler's Equation

An overview of methods for calculating the head of a rotodynamic impeller and their practical significance

2003 ◽  
Vol 217 (3) ◽  
pp. 221-232 ◽  
Author(s):  
S Yedidiah
Keyword(s):  
Subject Matter ◽  
Practical Significance ◽  
Euler’S Equation ◽  
Euler's Equation ◽  
The Subject

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.

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

1987 ◽  
Vol 201 (5) ◽  
pp. 357-363 ◽  
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.

On Darboux solutions of the Euler's equation

1989 ◽  
Vol 37 (2-3) ◽  
pp. 279-281
Author(s):  
J. Smítal
Keyword(s):  
Euler’S Equation ◽  
Euler's Equation
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