Complex Roots in the Characteristic Equation
نویسندگان
چکیده
منابع مشابه
Using Abel's Theorem to Explain Repeated Roots of the Characteristic Equation
This document describes how one can derive the solutions to a linear constant coefficient homogeneous differential equation with repeated roots in the characteristic equation with Abel’s Theorem.
متن کاملThe Characteristic Roots of a Matrix*
If A is a square matrix of order n and I is the unit matrix, the equation in X obtained by equating to zero the determinant \A— \l\ is called the characteristic equation of A. The roots of this equation are called the characteristic roots of A. Although it is not possible to make any definite statement as to the nature of the characteristic roots of the general algebraic matrix A, several autho...
متن کاملOn the roots of the trinomial equation
Here we summarize the works of the Hungarian mathematician Jenő Egerváry (1891–1958) on the trinomial equations. We present some of his ideas and methods with examples. Some earlier results in the history of mathematics in Hungary about the trinomial equations are also discussed.
متن کاملComment on "On the complex conjugate roots of the Rayleigh equation: the leaky surface wave".
In recent experiments and numerical studies, a leaky surface wave has been observed at the surface of an isotropic homogeneous elastic solid. This paper gives a detailed description of this leaky surface wave and explains its origin from the fundamental differential equations. Theoretically, the leaky surface wave arises from the complex conjugate roots of the Rayleigh equation. The complex con...
متن کاملCharacteristic Surface Data for the Eikonal Equation
A method of solving the eikonal equation, in either flat or curved space-times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front si...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Zisin (Journal of the Seismological Society of Japan. 2nd ser.)
سال: 1965
ISSN: 0037-1114,1883-9029,2186-599X
DOI: 10.4294/zisin1948.18.3_133