High Crosswind-Tolerance Airplane by Adjusting Dihedral Angle and Vertical Tail Volume

ABSTRACTA truncation of a Haar distributed orthogonal random matrix gives rise to a matrix whose eigenvalues are either real or complex conjugate pairs, and are supported within the closed unit disk. This is also true for a product Pm of m independent truncated orthogonal random matrices. One of most basic questions for such asymmetric matrices is to ask for the number of real eigenvalues. In this paper, we will exploit the fact that the eigenvalues of Pm form a Pfaffian point process to obtain an explicit determinant expression for the probability of finding any given number of real eigenvalues. We will see that if the truncation removes an even number of rows and columns from the original Haar distributed orthogonal matrix, then these probabilities will be rational numbers. Finally, based on exact finite formulas, we will provide conjectural expressions for the asymptotic form of the spectral density and the average number of real eigenvalues as the matrix dimension tends to infinity.

Multi-component diffusion and penetrative convection

Given three sets of $n$ real eigenvalues satisfying the trace equality and the Horn inequalities, we know that there are $n\times n$ real symmetric matrices $A$ and $B$ so that $A$ has the first set of eigenvalues, $B$ has the second set of eigenvalues, and $A+B$ has the last set of eigenvalues. Under the condition that $B$ is a rank 2 matrix, we give a construction for the matrices $A$ and $B$. This construction is based on performing two orthogonal rank 1 updates on $A$. We end with a discussion of the relationship between this rank 2 Horn problem and the following similar problem: given a set of $n$ real eigenvalues, a set of $2$ real eigenvalues, and a set of $n+2$ real eigenvalues satisfying certain conditions, find an $(n+2)\times(n+2)$ real symmetric matrix such that the top left principal submatrix has the first set of eigenvalues, the bottom right principal submatrix has the second set of eigenvalues, and the full matrix has the last set of eigenvalues.

A direct orthogonal equivalence transformation method for reordering the eigenvalues along the diagonal in the generalized real Schur form of a regular matrix pair (A, B) is presented. Each swap of two adjacent eigenvalues (real, or complex conjugate pairs) involves solving a generalized Sylvester equation and the construction of two orthogonal transformation matrices from certain eigenspaces associated with the corresponding diagonal blocks. An error analysis of the direct reordering method is presented. Results from numerical experiments on well-conditioned as well as ill-conditioned problems illustrate the stability and the accuracy of the method. Finally, a direct reordering algorithm with controlled backward error is described.

Complexified Pöschl–Teller II potential model

In this paper a recursive method of optimal pole placement of by weight selection is presented. First, a degree of stability by cost criterion modification is introduced. The method allows the allocation of both real and imaginary parts in the case of a complex conjugate pair.

At the broken phase of a parity-time (PT)-symmetric dimer where the coupling is weak, the eigenfrequencies are complex conjugate pairs with non-vanishing real parts, leading to oscillation magnitudes with an exponentially growing mode and an exponentially decaying mode. If the large oscillation magnitudes are clamped due to the nonlinear gain of the PT-symmetric dimer, the exponentially growing mode eventually enters the stable oscillations. It was recently demonstrated that such a phenomenon can be utilized for non-reciprocal transmission. The distortion induced by nonlinearity is critical for the non-reciprocal transmission. Here, we experimentally explore the nonlinear distortion in PT-symmetric inductor–capacitor resonators by utilizing discrete components on a printed circuit board. It demonstrates that the IIP3 (the output-referred third-order intercept point) can achieve as high as 38.7 dBm at the frequency of 14.5 MHz corresponding to the maximum forward transmission. The noise figure of the system is measured to be about 11.25 dB.

In this paper we address the modeling of long-memory signals with strong harmonic components. Current long-memory models, such as the fractional unit-pole model, fail to address the possibility of periodicities in the data. An example of harmonic long-memory signals is found in heart rate variability signals. We propose the harmonic fractional unit-pole model for modeling both the long-memory and harmonic components. The model is obtained by moving the fractional order pole on the unit circle away from zero frequency in a complex conjugate pair. The characteristics of the model, namely the power spectral density and the autocorrelation function are derived. A method is then given for the generation of harmonic long-memory signals. Finally the harmonic fractional unit-pole model is used to characterize heart rate variability signals.

Every real polynomial of degree n in one variable with root −1 can be represented as the Schur-Szegő composition of n − 1 polynomials of the form (x + 1) n−1(x + a i ), where the numbers a i are uniquely determined up to permutation. Some a i are real, and the others form complex conjugate pairs. In this note, we show that for each pair (ρ, r), where 0 ⩽ ρ, r ⩽ [n/2], there exists a polynomial with exactly ρ pairs of complex conjugate roots and exactly r complex conjugate pairs in the corresponding set of numbers a i .

Currently there is much interest in Hamiltonians that are not Hermitian but instead possess an antilinear PT symmetry. Here we seek to put such PT symmetric theories into as general a context as possible. After providing a brief overview of the PT symmetry program, we show that having an antilinear symmetry that acts on a well-defined Hilbert space is the most general condition that one can impose on a quantum theory for which one can have a well-defined inner product that is time independent, have a Hamiltonian that is self-adjoint, and have energy eigenvalues that are all real. For each of these properties Hermiticity is only a sufficient condition but not a necessary one, with Hermiticity thus being the special case in which the Hamiltonian has both antilinearity and Hermiticity. As well as being the necessary condition for the reality of energy eigenvalues, antilinearity in addition allows for the physically interesting cases of manifestly non-Hermitian but nonetheless self-adjoint Hamiltonians that have energy eigenvalues that appear in complex conjugate pairs, or that are Jordan block and cannot be diagonalized at all. We show that one can extend these ideas to quantum field theory, with the dual requirements of the existence of time independent inner products and invariance under complex Lorentz transformations forcing the antilinear symmetry to uniquely be CPT. We thus extend the CPT theorem to non-Hermitian Hamiltonians. For theories that are separately charge conjugation invariant, PT symmetry then follows, with the case for the physical relevance of the PT-symmetry program thus being advanced. While CPT symmetry can be defined at the classical level for every classical path in a path integral quantization procedure, in contrast, in such a path integral there is no reference at all to the Hermiticity of the Hamiltonian or the quantum Hilbert space on which it acts, as they are strictly quantum-mechanical concepts that can only be defined after the path integral quantization has been performed and the quantum Hilbert space has been constructed. CPT symmetry thus goes beyond Hermiticity and has primacy over it, with our work raising the question of how Hermiticity ever comes into quantum theory at all. To this end we show that whether or not a CPT-invariant theory has a Hamiltonian that is Hermitian is a property of the solutions to the theory and not of the Hamiltonian itself. Hermiticity thus never needs to be postulated at all.

Fundamental groups of fake projective planes fall into fifty distinct isomorphism classes, one for each complex conjugate pair. We prove that this is not the case for their algebraic fundamental groups: there are only forty-six isomorphism classes. We show that there are four pairs of complex conjugate pairs of fake projective planes that are \operatorname{Aut}(\mathbb{C}) -equivalent and hence have mutually isomorphic algebraic fundamental groups. All other pairs of algebraic fundamental groups are shown to be distinct through explicit finite étale covers. As a by-product, this provides the first examples of commensurable but nonisomorphic lattices in a rank one semisimple Lie group that have isomorphic profinite completions.

For stable systems, the eigenvalues are complex with a negative real part for underdamped modes. In this case, both the eigenvalues and eigenvectors occur in complex conjugate pairs and Eq. (18) can be expressed in real form by TV terms. In conclusion, this paper points out that the equations of motion of a flexible airplane can be written in the form of a general nonself-adjoint system which can be solved by the eigenfunction expansion.

This paper studies the design of a simulator to simulate the general behaviour of an aircraft in its lateral motion. The study will be in two parts: the aircraft lateral natural system and the design of the control laws. In the aircraft lateral natural system, all modes will be discussed including the Pure Roll mode, the Dutch Roll mode, and the Spiral mode. In the design of the control laws, two types of control laws were discussed which are the yaw damper and the poles placement method. The result is a complete simulator for aircraft lateral motion which allows the user to simulate and study the lateral characteristic of an aircraft given the desired input. The simulator resulted from this study is suitable to be used for teaching and learning as the changes in parameters yield instantaneous results that can be displayed.

The paper presents a six-degree of freedom mathematical model of a light sport aircraft and analytically reveals aircraft dynamic response both longitudinal and lateral-directional stability. The model composes of both the kinematics equations of motion and the kinetics equations of aerodynamic forces and moments, known as the aerodynamic model equations. Simulation results show responses of the perturbed dynamic system at trim condition, which indicates dynamic stability of both short-period pitching oscillation and phugoid in longitudinal axes. The spiral, roll subsidence, and dutch roll modes in lateral-directional axes are also dynamic stable as well. These are essential to understand and evaluate the dynamic behavior, stability, safety, and other aspects of the designed aircraft through a mathematical model before conducting an operational flight test.  

Mission of Unmanned Aerial Vehicle (UAV) “Elang Avionik” is surveillance and aerial photographs. Therefore the flight of UAV must be stable and controlable, and first step activity is dynamic modelling and stability analisys. The problems of UAV system is disturbance, noise of sensor, MIMO and uncertainty dynamic model. For good result using the multivariable robust control, with some step research that is: (1)modeling and stability analysis, (2) design and implementation of PID control system, (3) flight dynamic parameter identification, (4) design and implementation of hardware in the loop simulation, (5) design and implementation of multivariable robust control, (6) test and evaluation of system. Simulation result show that the eigen value in longitudinal is: phugoid mode = –0,061293±0,40526i and non-oscillation mode = –6,1121±4,9253. In lateral directional is:dutch roll mode = –0,91089±5,7994i, spiral mode= –0,036563, and roll subsidence mode = –12,7181. Location of poles system on the left of imaginary axis, the means that the character of system is dynamic stable. But settling time to steady state condition is very long and improved by control system design.
 Key word: State space, Longitudinal, Lateral, Stable static, Stable dynamic