This thesis details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic oscillations which are induced by sinusoidal excitations. The types of chaos are each associated with one of two homoclinic orbits in the system's phase portraits. The onset of each type of chaos is investigated through Melnikov's Method applied to the system's Hamiltonian, to find parameters at which the stable and unstable manifolds intersect transversely, indicating the onset of chaotic motion. These results are compared to simulation results, which suggest chaotic motion through the appearance of strange attractors in the Poincaré maps. Additionally, evidence of the WPP system experiencing both types of chaos simultaneously was found, resulting in a merger of two distinct types of strange attractor. / Master of Science / This report details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This system can be used to investigate what are known as local and global bifurcations. A local bifurcation occurs when the single equilibrium state (corresponding to the pendulum hanging straight down) when spun at low speeds, bifurcates into three equilibria when the spin rate is increased beyond a certain value. The global bifurcations occur when the system experiences sinusoidal forcing near certain equilibrium conditions. The resulting chaotic oscillations are investigated using Melnikov’s method, which determines when the sinusoidal forcing results in chaotic motion. This chaotic motion comes in two types, which cause the system to behave in different ways. Melnikov’s method, and results from a simulation were used to determine the parameter values in which the pendulum experiences each type of chaos. It was seen that at certain parameter values, the WPP experiences both types of chaos, supporting the observation that these types of chaos are not necessarily independent of each other, but can merge and interact.

This thesis presents the results of a research effort aimed at investigating the crash performance of w-beam guardrail barriers in vehicle-roadside crashes using the finite element method. The developed roadside barrier models can be used to assess the occupant injury risk, vehicle performance, and damage to guardrail barriers during a roadside accident. The finite element models of w-beam guardrail barriers may also help evaluate the crash performance of the w-beam barriers with minor damage in vehicle-barrier crashes. Thus, the results can be used to develop repair guidelines to assist highway personnel in identifying levels of minor barrier damage and deterioration. Finite element models of the weak post w-beam guardrail barriers were developed and simulated using LS-DYNA. The simulation results were validated against full scale crash tests of pickup trucks and passenger cars impacting w-beam guardrail barriers. The maximum dynamic deflection of the guardrail, exit velocity and angle of the vehicle, and occupant injury risk were calculated and compared to the tests. Kinematics of the vehicle and guardrail were assessed qualitatively as well as quantitatively. The analysis showed that simulation results were in good agreement with test data. Additionally, the models were validated against pendulum tests conducted the Federal Outdoor Impact Laboratory (FOIL). Simulation results of pendulum tests showed that the test section taken from the current full scale models performed very similarly to that in the real pendulum tests. The developed finite element models were subsequently used to examine the crash performance of weak post w-beam guardrail barriers with minor damage under vehicle impacts. Only rail/post deflection based minor damage to weak post w-beam guardrail barriers was considered in this study. Simulations were completed to obtain the damaged profiles of the guardrail systems; the damaged weak post guardrail barriers were impacted by the pickup model at mid-span for the second time. The impacting vehicle remained stable in all of these simulations. No conclusions could be drawn however whether these second impacts could have resulted in rail tearing or rupture. / Master of Science

O objetivo deste estudo foi avaliar, por meio das radiografias panorâmicas, o comportamento longitudinal da inclinação axial mesiodistal dos molares superiores decorridos cinco anos após o tratamento realizado com o aparelho Pendulum seguido de aparelhagem ortodôntica fixa e comparar os resultados com os valores médios normais. A amostra consistiu de 20 pacientes (14 do gênero feminino e 6, do masculino) com má oclusão de Classe II tratada por meio da distalização dos molares superiores. A média da idade, ao início do tratamento (T1), foi de 14,27 ± 1,62 anos, ao final do tratamento (T2), 18,59 ± 1,82 anos, e, cinco anos pós-tratamento (T3), 23,77 ± 2,04 anos. A média do tempo de tratamento foi de 4,36 ± 0,79 anos e de avaliação pós-tratamento foi de 5,18 ± 1,14 anos. Como grupo controle, utilizou-se os valores angulares médios normais de molares superiores obtidos por Ursi (1989), sendo que essa obtenção partiu de radiografias panorâmicas de indivíduos com oclusão normal apresentando idades entre 12 e 17 anos. Para a análise estatística, utilizaram-se os traçados das radiografias panorâmicas nas 3 fases (T1, T2 e T3). Os dados obtidos foram analisados estatisticamente pelo teste ANOVA dependente seguido do teste de Tukey. As médias das inclinações axiais mesiodistais nas fases T1, T2 e T3 foram comparadas com os valores médios normais pelo teste t independente. Os resultados apontaram que os primeiros molares superiores, ao término do tratamento ortodôntico, estavam mais inclinados para a distal, porém, cinco anos após, tenderam a verticalizarem-se naturalmente, voltando a ocupar uma posição próxima ao inicial. Quando comparados com os valores normais, somente o primeiro molar superior esquerdo apresentou, no período T2, valor estatisticamente significante diferente do normal. Os valores correspondentes para os segundos molares superiores não apresentaram estatisticamente significantes quando comparados entre si, nem quando comparados com os valores normais. O tratamento com o Pendulum seguido de aparelhagem ortodôntica fixa promove uma inclinação das coroas dos molares para a distal, tendendo esses dentes, entretanto, no longo tempo pós-tratamento, a verticalizarem-se. / The objective of this study was to evaluate, through panoramic radiographs, the longitudinal conduct of mesiodistal inclination in maxillary molars five years after the treatment performed with the Pendulum device followed by fixed appliance and compare the results with normal mean values. The sample consisted of 20 patients (14 female and 6 male) with Class II malocclusion treated with molar distalization. The average age at pretreatment (T1) was 14.27 ± 1.62 years, at posttreatment (T2), 18.59 ± 1.82 years and at the long-term posttreatment (T3) 23.77 ± 2.04 years. The average length of time of the treatment was 4.36 ± 0.79 years and the evaluation of the long-term posttreatment was 5.18 ± 1.14 years. As a control, it was used the normal mean angular values of molar obtained by Ursi (1989), and this achievement came from panoramic radiographs of subjects with normal occlusion ranging in age from 12 to 17 years. Panoramic radiographs were taken for statistic analysis in all 3 stages (T1, T2, T3). The obtained data were statistically analysed through ANOVA Test dependent followed by Tukey test. The mean mesiodistal axial inclinations stages T1, T2, T3 were compared with normal mean values by the independent t test. The results showed that the first molars were more inclined to distal at posttreatment but five years later they tended to upright naturally, occupying the previous position, close to the original. When compared with normal values, only the left first maxillary molar showed in T2 a statistically different value to the normal. The correspondent values for the second maxillary molars did not show to be statistically significant when compared with each other, nor when compared with normal values. The treatment with the Pendulum, together with the orthodontic appliance, fosters an inclination of the molars to the distal, but tends to upright in the long-term posttreatment.

O objetivo deste estudo foi avaliar, por meio das radiografias panorâmicas, o comportamento longitudinal da inclinação axial mesiodistal dos molares superiores decorridos cinco anos após o tratamento realizado com o aparelho Pendulum seguido de aparelhagem ortodôntica fixa e comparar os resultados com os valores médios normais. A amostra consistiu de 20 pacientes (14 do gênero feminino e 6, do masculino) com má oclusão de Classe II tratada por meio da distalização dos molares superiores. A média da idade, ao início do tratamento (T1), foi de 14,27 ± 1,62 anos, ao final do tratamento (T2), 18,59 ± 1,82 anos, e, cinco anos pós-tratamento (T3), 23,77 ± 2,04 anos. A média do tempo de tratamento foi de 4,36 ± 0,79 anos e de avaliação pós-tratamento foi de 5,18 ± 1,14 anos. Como grupo controle, utilizou-se os valores angulares médios normais de molares superiores obtidos por Ursi (1989), sendo que essa obtenção partiu de radiografias panorâmicas de indivíduos com oclusão normal apresentando idades entre 12 e 17 anos. Para a análise estatística, utilizaram-se os traçados das radiografias panorâmicas nas 3 fases (T1, T2 e T3). Os dados obtidos foram analisados estatisticamente pelo teste ANOVA dependente seguido do teste de Tukey. As médias das inclinações axiais mesiodistais nas fases T1, T2 e T3 foram comparadas com os valores médios normais pelo teste t independente. Os resultados apontaram que os primeiros molares superiores, ao término do tratamento ortodôntico, estavam mais inclinados para a distal, porém, cinco anos após, tenderam a verticalizarem-se naturalmente, voltando a ocupar uma posição próxima ao inicial. Quando comparados com os valores normais, somente o primeiro molar superior esquerdo apresentou, no período T2, valor estatisticamente significante diferente do normal. Os valores correspondentes para os segundos molares superiores não apresentaram estatisticamente significantes quando comparados entre si, nem quando comparados com os valores normais. O tratamento com o Pendulum seguido de aparelhagem ortodôntica fixa promove uma inclinação das coroas dos molares para a distal, tendendo esses dentes, entretanto, no longo tempo pós-tratamento, a verticalizarem-se. / The objective of this study was to evaluate, through panoramic radiographs, the longitudinal conduct of mesiodistal inclination in maxillary molars five years after the treatment performed with the Pendulum device followed by fixed appliance and compare the results with normal mean values. The sample consisted of 20 patients (14 female and 6 male) with Class II malocclusion treated with molar distalization. The average age at pretreatment (T1) was 14.27 ± 1.62 years, at posttreatment (T2), 18.59 ± 1.82 years and at the long-term posttreatment (T3) 23.77 ± 2.04 years. The average length of time of the treatment was 4.36 ± 0.79 years and the evaluation of the long-term posttreatment was 5.18 ± 1.14 years. As a control, it was used the normal mean angular values of molar obtained by Ursi (1989), and this achievement came from panoramic radiographs of subjects with normal occlusion ranging in age from 12 to 17 years. Panoramic radiographs were taken for statistic analysis in all 3 stages (T1, T2, T3). The obtained data were statistically analysed through ANOVA Test dependent followed by Tukey test. The mean mesiodistal axial inclinations stages T1, T2, T3 were compared with normal mean values by the independent t test. The results showed that the first molars were more inclined to distal at posttreatment but five years later they tended to upright naturally, occupying the previous position, close to the original. When compared with normal values, only the left first maxillary molar showed in T2 a statistically different value to the normal. The correspondent values for the second maxillary molars did not show to be statistically significant when compared with each other, nor when compared with normal values. The treatment with the Pendulum, together with the orthodontic appliance, fosters an inclination of the molars to the distal, but tends to upright in the long-term posttreatment.

The goal of this work is modelling and design of an inverted pendulum prototype. The work presents a mathematical model of a rotary pendulum, modelling of a BLDC motors and also a 3D model of the pendulum prototype is present. The work mentions design of the state space controller and swing up control of the inverted pendulum. Dynamics obtained from the mathematical model is used to create a 3D dynamic model of a pendulum, with the use of the Simscape toolbox. The work deals with control of a BLDC motors with use of vector control. The algorithm is implemented on the CompactRIO platform. Later, hardware is developed, containing STMicroelectronis microcontroller, capable of replacing the CompactRIO platform.

Thesis advisor: Andrzej Herczynski / The magnetic pendulum investigated in this experiment closely models various forms of the gravitational pendulum. However, the apparatus used in this experiment allows for greater insight as the constant and periodic forces can be easily varied. This project extends the previous work of Sang-Yoon Kim and Francis Moon on the magnetic pendulum by including an additional degree of freedom. This additional degree of freedom allows for a greater understanding of the bifurcation points observed. / Thesis (BS) — Boston College, 2007. / Submitted to: Boston College. College of Arts and Sciences. / Discipline: Physics. / Discipline: College Honors Program.

Intraarticular fractures (IAFs) are a leading cause of posttraumatic osteoarthritis (PTOA). Despite the latest orthopaedic treatment techniques, the risk of PTOA after IAFs has remained unacceptably high. In order to progress in this field, a new mechanical insult technique to create a large animal survival model of human IAF was developed. Current IAF models report the initial gravitational potential energy as the fracture energy value. However, this model included a pendulum device that was instrumented to accurately measure the amount of energy absorbed during fracture insult. After validating the energy absorption measurement with a mechanical testing machine and motion capture system, an in vivo study was conducted. The range of energy absorption measurements during fracture of the eleven animals was 11.7 é31.8 joules, with a mean and standard deviation of 20.8 ± 5.7 joules. On average, the energy absorption measurements were approximately 52 percent of the pre – impact kinetic energy values. These data showed that there was a substantial difference between the energy absorbed during fracture insult and the pre éimpact energy, which provided novel information associated with the pathomechanics of the induced injury.

The wave power converstion system nowadays nearly all have to depend on the converstion of mechanical energy.This way frequently causes unnecessary loss to the power.The costs of maintenance will also be high about the way. Therefore,we bring up a new wave power converstion system according to Faraday's Law.This way is no need to have the turbine.It can be catch the induced current from the generator directly. We use three different types of the PVC tubes as the model of the magnetic field and put into the round magnet.The motion of the round magnet will cause the change of the magnetic field to product the induced current.We install the magnet with the tube on a platform and combine them to be a structure.Different tubes, structure period and structure displasement will cause different effect of the generator.We apply to the data of experiments to find the relationship of the generator, structure period and structure displacement.We also use the neural network to build the model of the relationship. Finally, it will be the basis on the design of the real model in the future.

The Reaction Wheel Pendulum (RWP) is an interesting nonlinear system. A prototypical control problem for the RWP is to stabilize it around the upright position starting from the bottom, which is generally divided into at least 2 phases: (1) Swing-up phase: where the pendulum is swung up and moves toward the upright position. (2) Stabilization phase: here, the pendulum is controlled to be balanced around the upright position. Previous studies mainly focused on an energy method in swing-up phase and a linearization method in stabilization phase. However, several limitations exist. The energy method in swing-up mode usually takes a long time to approach the upright position. Moreover, its trajectory is not controlled which prevents further extensions. The linearization method in the stabilization phase, can only work for a very small range of angles around the equilibrium point, limiting its applicability. In this thesis, we took the 2nd order state space model and solved it for a constant torque input generating the family of phase-plane trajectories (see Appendix A). Therefore, we are able to plan the motion of the reaction wheel pendulum in the phase plane and a sliding mode controller may be implemented around these trajectories. The control strategy presented here is divided into three phases. (1) In the swing up phase a switching torque controller is designed to oscillate the pendulum until the system’s energy is enough to drive the system to the upright position. Our approach is more generic than previous approaches; (2) In the catching phase a sliding surface is designed in the phase plane based on the zero torque trajectories, and a 2nd order sliding mode controller is implemented to drive the pendulum moving along the sliding surface, which improves the robustness compared to the previous method in which the controller switches to stabilization mode when it reaches a pre-defined region. (3) In the stabilization phase a 2nd order sliding mode integral controller is used to solve the balancing problem, which has the potential to stabilize the pendulum in a larger angular region when compared to the previous linearization methods. At last we combine the 3 phases together in a combined strategy. Both simulation results and experimental results are shown. The control unit is National Instruments CompactRIO 9014 with NI 9505 module for module driving and NI 9411 module for encoding. The Reaction Wheel Pendulum is built by Quanser Consulting Inc. and placed in UT’s Advanced Mechatronics Lab. / text

Μεγάλο είναι το ερευνητικό ενδιαφέρον της εκπαιδευτικής κοινότητας για τις αντιλήψεις των μαθητών, που αφορούν στις έννοιες και τα φαινόμενα των φυσικών επιστημών. Αντιλήψεις, οι οποίες συγκροτούνται στη βάση της καθημερινής εμπειρίας και που παρέχουν στο μαθητή τη δυνατότητα να ερμηνεύει τα φαινόμενα του φυσικού κόσμου, συγκροτώντας επεξηγηματικά πρότυπα που, σε πολλές περιπτώσεις, έρχονται σε αντίθεση με τις επιστημονικές θεωρίες, που είναι σήμερα αποδεκτές. Από την άλλη πλευρά, η καινοτομική αντίληψη για τη μάθηση και τη διδασκαλία των φυσικών επιστημών, θεωρεί ότι η ανάπτυξη της επιστημονικής καλλιέργειας των μαθητών και των εκπαιδευτικών, αναφέρεται στη διάδοση των τριών βασικών συνιστωσών της επιστημονικής γνώσης: - της εννοιολογικής συνιστώσας, που συγκροτείται από τις έννοιες των φυσικών επιστημών, - της μεθοδολογικής συνιστώσας, που σχετίζεται με τις διάφορες μεθοδολογικές στρατηγικές και τεχνικές με τις οποίες επιλύονται τα προβλήματα στις φυσικές επιστήμες και - της πολιτισμικής συνιστώσας, που αφορά στο σύνολο των σχέσεων που αναπτύσσουν οι φυσικές επιστήμες με την κοινωνία, όπως για παράδειγμα η σχέση των φυσικών επιστημών με την τεχνολογία, τα προβλήματα και τις εμπειρίες της καθημερινής ζωής, η κατανόηση της ιστορικότητας της επιστημονικής γνώσης κ.α. Η μελέτη του απλού εκκρεμούς, χαρακτηρίζεται από το πλούσιο εννοιολογικό, μεθοδολογικό και πολιτισμικό περιεχόμενο, που αυτό παρουσιάζει. Η μελέτη της κίνησης του, δίνει την ευκαιρία στους μαθητές: - Να έρθουν σε επαφή με θεμελιώδεις επιστημονικές γνώσεις, όπως οι νόμοι της πτώσης και της κίνησης και οι αρχές διατήρησης της ορμής και της ενέργειας. - Να ασκηθούν στη χρήση ουσιαστικών στοιχείων της επιστημονικής έρευνας, όπως η παρατήρηση, η μέτρηση, η συλλογή δεδομένων, ο έλεγχος μεταβλητών και η χρήση διαφόρων μορφών μαθηματικών αναπαραστάσεων. - Να μάθουν σημαντικές όψεις της συσχέτισης της επιστήμης με την κοινωνία, τον πολιτισμό και την τεχνολογία, όπως φανερώνει η χρήση του εκκρεμούς στη χρονομέτρηση, στον προσδιορισμό του γεωγραφικού μήκους, στον καθορισμό μονάδας μέτρησης του μήκους κ.α. Η παρούσα εργασία, έχει ως στόχο τη διερεύνηση των βιωματικών αντιλήψεων των μαθητών της Γ’ Γυμνασίου, που αφορούν στη μέτρηση του χρόνου με τρεις ιστορικούς μηχανισμούς μέτρησης του χρόνου και στη μελέτη της κίνησης του απλού εκκρεμούς. Ειδικότερα, διερευνώνται οι αντιλήψεις των μαθητών που σχετίζονται με την εννοιολογική, τη μεθοδολογική και την πολιτισμική συνιστώσα της γνώσης που σχετίζεται με την ισόχρονη κίνηση του απλού εκκρεμούς. Στο πρώτο κεφάλαιο, παρουσιάζεται το θεωρητικό πλαίσιο της έρευνας, που απαρτίζεται από: - τη γνώση αναφοράς, δηλαδή το ιστορικό πρόβλημα της μέτρησης του χρόνου και τη σχέση του με το απλό εκκρεμές, - τις αντιλήψεις των μαθητών για το απλό εκκρεμές και - τους στόχους της έρευνας. Στο δεύτερο κεφάλαιο, παρουσιάζεται η μεθοδολογική προβληματική της μελέτης, που αφορά: - στις στρατηγικές και - στο δείγμα της έρευνας. Στο τρίτο κεφάλαιο, παρουσιάζονται τα αποτελέσματα της ανάλυσης των δεδομένων. Τέλος, στο τέταρτο κεφάλαιο, διατυπώνονται τα συμπεράσματα της μελέτης των αντιλήψεων των μαθητών, στη βάση των ερευνητικών στόχων και συζητούνται οι ενδεχόμενες επιπτώσεις τους στη διδασκαλία του απλού εκκρεμούς στην εκπαιδευτική βαθμίδα του γυμνασίου, καθώς και μία πρόταση επέκτασης της έρευνας. / -