Rigid Body Dynamics using Equimomental Systems of Point-Masses

The inertia matrix of any rigid body is the same as the inertia matrix of some system of four point-masses. In this work the possible disposition of these point-masses is investigated. It is found that every system of possible point-masses with the same inertia matrix can be parameterised by the elements of the orthogonal group in four dimensions modulo permutation of the points. It is shown that given a fixed inertia matrix, it is possible to find a system of point-masses with the same inertia matrix but where one of the points is located at some arbitrary point. It is also possible to place two point-masses on an arbitrary line or three of the points on an arbitrary plane. The possibility of placing some of the point- masses at infinity is also investigated. Applications of these ideas to rigid-body dynamics is considered. The equation of motion for a rigid body is derived in terms of a system of four point-masses. These turn out to be very simple when written in a 6-vector notation

On the Exponentials of Some Structured Matrices

In this note explicit algorithms for calculating the exponentials of important structured 4 x 4 matrices are provided. These lead to closed form formulae for these exponentials. The techniques rely on one particular Clifford Algebra isomorphism and basic Lie theory. When used in conjunction with structure preserving similarities, such as Givens rotations, these techniques extend to dimensions bigger than four.Comment: 19 page

The development of an accreditation scheme for accredited exercise physiologists

Background: Accredited Exercise Physiologists provide exercise services for people living with chronic disease, disability or injury and are recognised in Australia as Accredited Exercise Physiologists (AEP) under a national certification system administered by Exercise and Sport Science Australia (ESSA). A major breakthrough occurred for the AEP in 2006 when the Australian Department of Health and Ageing approved the AEP to deliver clinical exercise services for people with chronic medical conditions under the taxpayer-funded national health scheme, Medicare Australia. Aims: In light of these developments, the authors recognised the need for new accreditation criteria, and our report summarises the work that we did on behalf of the profession and ESSA in restructuring the accreditation system. Methods and Outcomes: We first performed a background study that defined the scope of practice of the AEP and benchmarked the AEP against other allied health professions in Australia and Clinical Exercise Physiologists internationally. We then constructed a new set of accreditation criteria comprising sets of pathologyspecific knowledge and experiences, together with a set of generic standards including communication, professional behaviour and risk management. All participating Australian universities (18 out of 27 responded) and 29 practitioner experts were then invited to provide comment and input into the draft guidelines. There was strong support for the new system that was implemented nationally on 1 January 2008 and is now administered by ESSA. Conclusions: This work has stimulated an unprecedented level of activity in the Australian university sector in developing new curricula in clinical exercise science and practice, and is intended to lead to improved standards of clinical exercise practice.<br /

Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping

Comparing methods for prescribing exercise for individuals with chronic heart failure

This study examined the accuracy of current recommended guidelines for prescribing exercise intensity using the methods of percentage of heart rate reserve (%HRR), percentage of VO2 peak (%VO2peak) and percentage of VO2 reserve (%VO2R) in a clinical population of chronic heart failure (CHF) patients. The precision of prescription of exercise intensity for 45 patients with stable CHF (39:6 M:F, 65&plusmn;9 yrs (mean&plusmn;SD)) was investigated. VO2peak testing is relatively common among patients with cardiac disease, but the assessment of VO2rest is not common practice and the accepted standard value of 3.5 mL/kg/min is assumed in the application of %VO2R (%VO2R3.5). In this study, VO2rest was recorded for 3 min prior to the start of a symptom-limited exercise test on a cycle ergometer. Target exercise intensities were calculated using the VO2 corresponding to 50 or 80 %HRR, VO2peak and VO2R. The VO2 values were then converted into prescribed speeds on a treadmill in km/hr at 1 %grade using ACSM&rsquo;s metabolic equation for walking. Target intensities and prescribed treadmill speeds were also calculated with the %VO2R method using the mean VO2rest value of participants (3.9 mL/kg/min) (%VO2R3.9). This was then compared to the exercise intensities and prescribed treadmill speeds using patient&rsquo;s measured VO2rest. Error in prescription correlates the difference between %VO2R3.5 and %VO2R3.9 compared to %VO2R with measured VO2rest. Prescription of exercise intensity through the %HRR method is imprecise for patients on medications that blunt the HR response to exercise. %VO2R method offers a significant improvement in exercise prescription compared to %VO2peak. However, a disparity of 10 % still exists in the %VO2R method using the standard 3.5 mL/kg/min for VO2rest in the %VO2R equation. The mean measured VO2rest in the 45 CHF patients was 11 % higher (3.9&plusmn;0.8 mL/kg/min) than the standard value provided by ACSM. Applying the mean measured VO2rest value of 3.9 mL/kg/min rather than the standard assumed value of 3.5 mL/kg/min proved to be closer to the prescribed intensity determined by the actual measured resting VO2. These results suggest that the %HRR method should not be used to prescribe exercise intensity for CHF patients. Instead, VO2 should be used to prescribe exercise intensity and be expressed as %VO2R with measured variables (VO2rest and VO2peak).<br /

Assessing the value of BMI and aerobic capacity as surrogate markers for the severity of left ventricular diastolic dysfunction in patients with type 2 diabetes who are obese

Left ventricular diastolic dysfunction (LVDD) is one of the earliest signs for abnormal cardiac function in patients with type 2 diabetes (T2DM). It is important to explore the risk factors that will assist in identifying the severity of the LVDD in this population. We examined the influences of fitness and fatness on the level of left ventricular (LV) impairment in patients with T2DM. Twenty-five patients (age: 64.0 &plusmn; 2.5 years, body mass index [BMI] = 36.0 &plusmn; 1.5 kg/m2, mean &plusmn; standard error of measurement) with T2DM and preserved systolic function, but impaired diastolic function, mitral valve (MV) E/e\u27, participated in the study. LV function was assessed using a stress echocardiograph, aerobic power was assessed with a sign- and symptom-limited graded exercise test, and the fatness level was assessed using Dual-energy X-ray absorptiometry and BMI. Patients in the higher 50% of BMI had higher lateral and septal MV E/e\u27 (&sim;34% and &sim;25%, respectively, both P &lt; 0.001), compared to those in the lower 50% of BMI, with no difference in LV ejection fraction (LVEF) (P &gt; 0.05). In addition, a higher BMI correlated with a higher lateral (r = 0.62, P &lt; 0.001) and septal (r = 0.56, P &lt; 0.01) E/e\u27. There was no such relationship for VO2peak. BMI and VO2peak were not correlated with LV systolic function (ejection fraction). In individuals with T2DM and diastolic dysfunction, a higher BMI was associated with worsening diastolic function independent of their aerobic capacity. The data provide a simple and practical approach for clinicians to assist in the early identification and diagnostics of functional changes in the heart diastolic function in this population

Towards a model of port-based resilience against fisher labour exploitation

Fishers have pronounced vulnerabilities to labour exploitation and modern slavery. Regulatory efforts to mitigate fisher labour exploitation through domestic modern slavery legislation, and through the ratification and implementation of The International Labour Organization's Work in Fishing Convention (C188) have had varying success. This heterogeneity is mainly because the implementation of C188 rests upon ratified states enforcing aligned domestic legislation, and rests also on the supposition that each port state has the resources and capacity to implement these standards within its port networks through enforcement levers and agencies often with varying operational reach and with overlapping jurisdictions. In practice, C188 applies messily and variably in ports. Increasingly ports are cast as fulcrums for addressing labour abuses in fishing, yet policies have struggled to connect together the needs of individual fishers with relevant port structures and services in a meaningful and actionable way. This paper advances a conceptual model for conducting a port-by-port analysis of port communities by appraising site-based assets and dynamics. With this understanding, a port-based and place-specific account of fisher vulnerability and resilience can be constructed. This analysis also considers how regulatory coverage and enforcement can be supplemented by the operationalisation of a multi-factored, multi-scalar consideration of risk determinants. Together this dynamic asset and liability-based model of port resilience can better reflect the variability of port enforcement, capacity, and infrastructure to more effectively assess fisher labour exploitation and identify pathways for improved enforcement