The comfortable roller coaster -- on the shape of tracks with constant normal force

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.Comment: 10 pages, 4 figure

Chatter, sticking and chaotic impacting motion in a two-degree of freedom impact oscillator

We consider the dynamics of a two-degree of freedom impact oscillator subject to a motion limiting constraint. These systems exhibit a range of periodic and nonperiodic impact motions. For a particular set of parameters, we consider the bifurcations which occur between differing regimes of impacting motion and in particular those which occur due to a grazing bifurcation. Unexpected resonant behavior is also observed, due to the complexity of the dynamics. We consider both periodic and chaotic chatter motions and the regions of sticking which exist. Finally we consider the types of chaotic motion that occur within the parameter range. We discuss the possibility in relating successive low velocity impacts, especially with respect to possible low dimensional mappings for such a system

Researching "British [Muslim] Values": Vernacular politics, digital storytelling, and participant researchers

This article reflects on methodological decisions, strategies, and challenges from a recent interdisciplinary project on the relationship between ‘British values’ and Islam. The project employed digital storytelling to access ‘everyday’ conceptions and constructions of this contentious relationship. The research was undertaken by participant researchers recruited from Muslim communities in the UK’s East Anglia region, working with academics from media studies and political science. In this article we offer a detailed account of key moments relating especially to recruitment, retention, and the production of digital content. It offers two contributions. First, methodological guidance for researchers interested in combining participatory research with digital storytelling. And, second, rationale for so doing given the methodology’s scope for producing rich visual content with capacity (i) to deepen and disrupt established knowledge, and (ii) to change the views, ideas and aspirations of those involved in the content’s creation

Rotating strings

Analytical expressions are provided for the configurations of an inextensible, flexible, twistable inertial string rotating rigidly about a fixed axis. Solutions with trivial radial dependence are helices of arbitrary radius and pitch. Non-helical solutions are governed by a cubic equation whose roots delimit permissible values of the squared radial coordinate. Only curves coplanar with the axis of rotation make contact with it.Comment: added to discussion and made small revisions to tex

Development of lower limb range of motion from early childhood to adolescence in cerebral palsy: a population-based study

<p>Abstract</p> <p>Background</p> <p>The decreasing range of joint motion caused by insufficient muscle length is a common problem in children with cerebral palsy (CP), often worsening with age. In 1994 a CP register and health care programme for children with CP was initiated in southern Sweden. The aim of this study was to analyse the development of the passive range of motion (ROM) in the lower limbs during all the growth periods in relation to gross motor function and CP subtype in the total population of children with CP.</p> <p>Methods</p> <p>In total, 359 children with CP born during 1990-1999, living in the southernmost part of Sweden in the year during which they reached their third birthday and still living in the area in the year of their seventh birthday were analysed. The programme includes a continuous standardized follow-up with goniometric measurements of ROM in the lower limbs. The assessments are made by each child's local physiotherapist twice a year until 6 years of age, then once a year. In total, 5075 assessments from the CPUP database from 1994 to 1 January 2007 were analysed.</p> <p>Results</p> <p>The study showed a decreasing mean range of motion over the period 2-14 years of age in all joints or muscles measured. The development of ROM varied according to GMFCS level and CP subtype.</p> <p>Conclusion</p> <p>We found a decreasing ROM in children with CP from 2-14 years of age. This information is important for both the treatment and follow-up planning of the individual child as well as for the planning of health care programmes for all children with CP.</p

Long-term outcomes five years after selective dorsal rhizotomy

<p>Abstract</p> <p>Background</p> <p>Selective dorsal rhizotomy (SDR) is a well accepted neurosurgical procedure performed for the relief of spasticity interfering with motor function in children with spastic cerebral palsy (CP). The goal is to improve function, but long-term outcome studies are rare. The aims of this study were to evaluate long-term functional outcomes, safety and side effects during five postoperative years in all children with diplegia undergoing SDR combined with physiotherapy.</p> <p>Methods</p> <p>This study group consisted of 35 children, consecutively operated, with spastic diplegia, of which 26 were Gross Motor Function Classification System (GMFCS) levels III–V. Mean age was 4.5 years (range 2.5–6.6). They were all assessed by the same multidisciplinary team at pre- and at 6, 12, 18 months, 3 and 5 years postoperatively. Clinical and demographic data, complications and number of rootlets cut were prospectively registered. Deep tendon reflexes and muscle tone were examined, the latter graded with the modified Ashworth scale. Passive range of motion (PROM) was measured with a goniometer. Motor function was classified according to the GMFCS and measured with the Gross Motor Function Measure (GMFM-88) and derived into GMFM-66. Parent's opinions about the children's performance of skills and activities and the amount of caregiver assistance were measured with Pediatric Evaluation Disability Inventory (PEDI).</p> <p>Results</p> <p>The mean proportion of rootlets cut in S2-L2 was 40%. Muscle tone was immediately reduced in adductors, hamstrings and dorsiflexors (p < 0.001) with no recurrence of spasticity over the 5 years. For GMFCS-subgroups I–II, III and IV–V significant improvements during the five years were seen in PROM for hip abduction, popliteal angle and ankle dorsiflexion (p = 0.001), capacity of gross motor function (GMFM) (p = 0.001), performance of functional skills and independence in self-care and mobility (PEDI) (p = 0.001).</p> <p>Conclusion</p> <p>SDR is a safe and effective method for reducing spasticity permanently without major negative side effects. In combination with physiotherapy, in a group of carefully selected and systematically followed young children with spastic diplegia, it provides lasting functional benefits over a period of at least five years postoperatively.</p

Growth in Children with Cerebral Palsy during five years after Selective Dorsal Rhizotomy: a practice-based study

Background: Overweight is reported as a side effect of SDR. The aims were to study the development of weight, height and body mass index (BMI) during five years after SDR. Methods: This prospective, longitudinal and practice-based study included all 56 children with CP spastic diplegia undergoing SDR from the start in March 1993 to April 2003 in our hospital. The preoperative Gross Motor Function Classification System (GMFCS) levels were I-II in 17, III in 15, IV-V in 24 children. Median age at SDR was 4.3 years (range 2.4-7.4 years). Weight and height/recumbent length were measured. Swedish growth charts for typically developing children generated weight, height and BMI z-scores for age and gender. Results: The preoperative median z-scores were for height-1.92 and for body mass index (BMI)-0.22. Five years later, the median BMI z-score was increased by + 0.57 (p + 2 SD) increased (p < 0.05). Baseline BMI and age at the start of follow-up influenced the BMI change during the five years (p < 0.001 and p < 0.05 respectively). The individual growth was highly variable, but a tendency towards increasing stunting with age was seen in severe gross motor dysfunction (GMFCS levels IV-V) and the opposite, a slight catch-up of height in children with walking ability (GMFCS levels I-III). Conclusions: These are the first available subtype-and GMFCS-specific longitudinal growth data for children with CP spastic diplegia. Their growth potential according to these data should be regarded as a minimum, as some children were undernourished. It is unknown whether the spasticity reduction through SDR increased the weight gain velocity, or if the relative weight increase was part of the general "obesity epidemic". For some children the weight increase was highly desirable. In others, it resulted in overweight and obesity with risk of negative health effects. Weight and height should be monitored to enable early prevention of weight aberrations also causing problems with mobility, activity and participation

Association between gross motor function (GMFCS) and manual ability (MACS) in children with cerebral palsy. A population-based study of 359 children

<p>Abstract</p> <p>Background</p> <p>The Gross Motor Function Classification System (GMFCS) has become an important tool to describe motor function in children with Cerebral Palsy (CP). The Manual Ability Classification System (MACS) was developed recently as a corresponding classification of manual ability. The aim of this study was to describe the association between gross motor function and manual ability in a total population of children with cerebral palsy.</p> <p>Methods</p> <p>365 children, born 1992 to 2001, who were registered in a population-based health care programme (CPUP) for children with CP living in the south of Sweden were included in the study. GMFCS was evaluated by the child's physiotherapist and MACS by the occupational therapist. CP diagnosis and subtype were determined by the neuropaediatrician at or after the age of four.</p> <p>Results</p> <p>GMFCS levels were available in all 365 children, MACS levels in 359 (98%). There was a poor overall correlation between gross motor function and manual ability. However, different associations between gross motor function and manual ability were found in the different diagnostic subtypes. Children with spastic hemiplegia generally had a lower level of manual ability than gross motor function (p < 0.001). The reverse association was generally found in children with spastic diplegia (p < 0.001). Children with dyskinetic CP had large limitations in both gross motor function and manual ability, with no significant discrepancy between GMFCS and MACS levels.</p> <p>Conclusion</p> <p>Gross motor function and manual ability are often discrepant in children with CP, and the patterns seem to vary across the different subgroups based on the predominant neurological findings. To give a complete clinical picture when evaluating these children, both aspects have to be described. The GMFCS and the MACS seem to work well in this context and seem very useful in population-based studies, in health care registers for children with CP, and in clinical practice.</p

Systemic manifestations of primary Sjögren's syndrome out of the ESSDAI classification: prevalence and clinical relevance in a large international, multi-ethnic cohort of patients

OBJECTIVES: To analyse the frequency and characterise the systemic presentation of primary Sjögren’s syndrome (SS) out of the ESSDAI classification in a large international, multi-ethnic cohort of patients. // METHODS: The Big Data Sjögren Project Consortium is an international, multicentre registry based on world-wide data-sharing and cooperative merging of pre-existing clinical SS databases from leading centres in clinical research in SS from the five continents. A list of 26 organ-by-organ systemic features not currently included in the ESSDAI classification was defined according to previous studies; these features were retrospectively recorded. // RESULTS: Information about non-ESSDAI features was available in 6331 patients [5,917 female, mean age at diagnosis 52 years, mainly White (86.3%)]. A total of 1641 (26%) patients had at least one of the ESSDAI systemic features. Cardiovascular manifestations were the most frequent organ-specific group of non-ESSDAI features reported in our patients (17% of the total cohort), with Raynaud’s phenomenon being reported in 15%. Patients with systemic disease due to non-ESSDAI features had a lower frequency of dry mouth (90.7% vs. 94.1%, p<0.001) and positive minor salivary gland biopsy (86.7% vs. 89%, p=0.033), a higher frequency of anti-Ro/SSA (74.7% vs. 68.7%, p<0.001), anti-La/SSB antibodies (44.5% vs. 40.4%, p=0.004), ANA (82.7% vs. 79.5%, p=0.006), low C3 levels (17.4% vs. 9.7%, p<0.001), low C4 levels (14.4% vs. 9.6%, p<0.001), and positive serum cryoglobulins (8.6% vs. 5.5%, p=0.001). Systemic activity measured by the ESSDAI, clinESSDAI and DAS was higher in patients with systemic disease out of the ESSDAI in comparison with those without these features (p<0.001 for all comparisons). // CONCLUSIONS: More than a quarter of patients with primary SS may have systemic manifestations not currently included in the ESSDAI classification, with a wide variety of cardiovascular, digestive, pulmonary, neurological, ocular, ENT (ear, nose, and throat), cutaneous and urological features that increase the scope of the systemic phenotype of the disease. However, the individual frequency of each of these non-ESSDAI features was very low, except for Raynaud’s phenomenon