Analytical solutions of the simplified Mathieu’s equation
Journal Title: INCAS BULLETIN - Year 2016, Vol 8, Issue 1
Abstract
Consider a second order differential linear periodic equation. The periodic coefficient is an approximation of the Mathieu’s coefficient. This equation is recast as a first-order homogeneous system. For this system we obtain analytical solutions in an explicit form. The first solution is a periodic function. The second solution is a sum of two functions, the first is a continuous periodic function, but the second is an oscillating function with monotone linear increasing amplitude. We give a formula to directly compute the slope of this increase, without knowing the second numeric solution. The periodic term of the second solution may be computed directly. The coefficients of fundamental matrix of the system are analytical functions.
Authors and Affiliations
Nicolae MARCOV
Keywords
Related Articles
- EP ID EP148983
- DOI 10.13111/2066-8201.2016.8.1.11
- Views 56
- Downloads 0
Nonlinear automatic control of the satellites by using the quaternion and the angular velocities’ vectors
In this paper, the authors propose a new architecture for the control of the satellites’ attitude by using a control law mainly based on a proportional-integrator component with respect to the quaternion vector and to th...
Safety management of formation flying in an aerobatic team
The article is focused on explaining the notion of safety from the aspect of generally applicable standards established by the ICAO. It describes the role of human factor played by the pilot´s personality in an aerobatic...
An Analytic Potential Solution for Incompressible 2D Channel Inviscid Flow with Wall Injection
The present paper introduces an analytical potential solution for the incompressible flow in a 2D channel with normal wall injection. This solution is capable to support reasonable injection flow rates as compared to the...
Methodologies of Measuring Mechanical Power Delivered at the Shaft of an Induction Motor Driven by VFD
Measuring precise power used by a load of an induction motor driven by a VFD implies a few facts that need to be considered. First, the real electric power. When dealing with waveforms of electric current that contain ha...
Towards spacecraft applications of structural health monitoring
The first part of the paper presents recent developments in the field of structural health monitoring (SHM) with special attention on the piezoelectric wafer active sensors (PWAS) technologies utilizing guided waves (GW)...