Search results for "Legendre polynomials"
showing 10 items of 19 documents
Partial Stabilization of Input-Output Contact Systems on a Legendre Submanifold
2017
This technical note addresses the structure preserving stabilization by output feedback of conservative input-output contact systems, a class of input-output Hamiltonian systems defined on contact manifolds. In the first instance, achievable contact forms in closed-loop and the associated Legendre submanifolds are analysed. In the second instance the stability properties of a hyperbolic equilibrium point of a strict contact vector field are analysed and it is shown that the stable and unstable manifolds are Legendre submanifolds. In the third instance the consequences for the design of stable structure preserving output feedback are derived: in closed-loop one may achieve stability only rel…
Thermo-mechanical post-buckling analysis of variable angle tow composite plate assemblies
2017
peer-reviewed The increasing use of composite materials for lightweight structural applications and the extended tailoring capabilities offered by variable stiffness laminates requires rapid and robust analysis tools that adequately describe the mechanical behaviour of such structures. In this work, a Rayleigh–Ritz solution for generally restrained multilayered stiffened variable angle tow plates in the post-buckling regime is presented. The plate model is based on first-order shear deformation theory and accounts for geometrical nonlinearity through von Kármán’s assumptions. General symmetric and unsymmetric stacking sequences are considered and Legendre orthogonal polynomials are employed…
Error analysis of the orthogonal series solution of linear time-invariant systems
1989
Similarities in the error analysis of the polynomial series solution of linear time-invariant systems are pointed out.
Real symplectic formulation of local special geometry
2006
We consider a formulation of local special geometry in terms of Darboux special coordinates $P^I=(p^i,q_i)$, $I=1,...,2n$. A general formula for the metric is obtained which is manifestly $\mathbf{Sp}(2n,\mathbb{R})$ covariant. Unlike the rigid case the metric is not given by the Hessian of the real function $S(P)$ which is the Legendre transform of the imaginary part of the holomorphic prepotential. Rather it is given by an expression that contains $S$, its Hessian and the conjugate momenta $S_I=\frac{\partial S}{\partial P^I}$. Only in the one-dimensional case ($n=1$) is the real (two-dimensional) metric proportional to the Hessian with an appropriate conformal factor.
On an Inequality for Legendre Polynomials
2020
This paper is concerned with the orthogonal polynomials. Upper and lower bounds of Legendre polynomials are obtained. Furthermore, entropies associated with discrete probability distributions is a topic considered in this paper. Bounds of the entropies which improve some previously known results are obtained in terms of inequalities. In order to illustrate the results obtained in this paper and to compare them with other results from the literature some graphs are provided.
Landau parameters for energy density functionals generated by local finite-range pseudopotentials
2017
In Landau theory of Fermi liquids, the particle-hole interaction near the Fermi energy in different spin-isospin channels is probed in terms of an expansion over the Legendre polynomials. This provides a useful and efficient way to constrain properties of nuclear energy density functionals in symmetric nuclear matter and finite nuclei. In this study, we present general expressions for Landau parameters corresponding to a two-body central local regularized pseudopotential. We also show results obtained for two recently adjusted NLO and N$^2$LO parametrizations. Such pseudopotentials will be used to determine mean-field and beyond-mean-field properties of paired nuclei across the entire nucle…
Exclusive deuteron electrodisintegration with polarized electrons and a polarized target
1992
Exclusive electrodisintegration of the deuteron using a polarized beam and an oriented target is systematically investigated in a nonrelativistic framework. The structure functions are expanded in terms of Legendre functions whose coefficients are quadratic forms in the electric and magnetic multipole moments. Their experimental separation by specific experimental settings is outlined. The structure functions are studied with respect to their sensitivity to the potential model, to subnuclear degrees of freedom, and to electromagnetic form factors in different kinematical regions.
Formal theory for two-particle channels
1991
The general formalism has been developed over many years by various authors. One starting point is the work of de Swart (DSw 59) who has considered electric multipoles in the long-wave-length limit using the Siegert theorem and as magnetic contribution only the dipole spin-flip transition. The T-matrix is then expanded in terms of reduced multipole amplitudes. This approach has been generalized by Donnachie (Don 62a) and Partovi (Par 64) by including higher electric and magnetic multipoles. Furthermore, the electric multipoles are not restricted to the long-wave-length limit and the additional terms besides the Siegert operators (see section 4.1) are included. Using techniques from angular …
Analytical Solutions for the Self- and Mutual Inductances of Concentric Coplanar Disk Coils
2013
In this paper, closed-form solutions are presented for the self- and mutual inductances of disk coils which lie concentrically in a plane. The solutions are given as generalized hypergeometric functions which are closely related to elliptic integrals. The method used is a Legendre polynomial expansion of the inductance integral, which renders all integrations straightforward. Excellent numerical agreement with previous studies is obtained. An asymptotic formula for the approach to the ring coil limit is also derived and numerically validated. The methods presented here can be applied to noncoaxial and noncoplanar cases.
Zone plates with cells apodized by Legendre profiles
1990
By apodizing the cells of a zone plate and changing the opening ratio, it is possible to shape the relative power spectrum of its foci. We describe a novel procedure that leads to an analytical formula for shaping the focus power spectrum by using apodizers expressible as the Legendre series; these act on cells of arbitrary opening ratio. Our general result is used to design zone plates that have missing foci and to discuss a synthesis procedure using apodizers with various opening ratios. Our applications can also be used for shaping the power spectrum of 1-D gratings.