11 research outputs found
ε^2-Order normal form analysis for a two-degree-of-freedom nonlinear coupled oscillator
In this paper, we describe an ε^2-order normal form decomposition for a two-degree-of-freedom oscillator system that has a mass supported with horizontal and vertical support springs. This system has nonlinear terms that are not necessarily ε^1-order small when compared to the linear terms. As a result, analytical approximate methods based on an ε expansion would typically need to include higher-order components in order to capture the nonlinear dynamic behaviour. In this paper we show how this can be achieved using a direct normal form transformation up to order ε^2. However, we will show that the requirement for including ε^2 components is primarily due to the way the direct normal form method deals with quadratic coupling terms rather than the relative size of the coefficients
Global Persistence of Lyapunov Subcenter Manifolds as Spectral Submanifolds under Dissipative Perturbations
Combined single-photon emission computerized tomography and conventional computerized tomography (SPECT/CT) : clinical value for the knee surgeons?
Single-photon emission computerized tomography in combination with conventional computer tomography (SPECT/CT) is an emerging technology that may hold great clinical value to the orthopaedic knee surgeon. Post-operative knee pain is a familiar condition seen in most orthopaedic clinics. Here, we present the value of SPECT/CT in three such cases of pain after surgical treatment of knee osteoarthritis (high tibial osteotomy, medial unicompartmental arthroplasty, total knee arthroplasty). In these patients with post-operative knee pain, SPECT/CT has proved to be beneficial in establishing the diagnosis and providing guidance for further treatment