The vibrational entropy calculated by applying the harmonic oscillator approximation to all vibrational degrees of freedom is inherently inaccurate. One major reason is because low frequency modes such as internal rotations are not properly described by this approximation. Various techniques were developed in the past to overcome this problem. The hindered rotor potential can be approximated by a series of cosine functions, and the relevant coe cients can be determined by tting to a calculated potential energy surface. However, such a method is di cult and time consuming. Therefore, in this dissertation we propose and describe two less tedious approaches to determine entropy of internal rotational modes. The rst approximation is to express the barrier height in terms of the harmonic oscillator frequency, the local periodicity, and the reduced moment of inertia of the rotation and to approximate the torsional potential by a single cosine function. Thus, the 1D Schr odinger equation for internal rotations can be solved without nding the torsional potential, transition states, or barrier heights. We propose a further simpli cation to this approach, achieved through a simple mathematical formula, that interpolates the hindered rotor entropy between the free rotor and harmonic oscillator limits. We also propose a procedure to automatically determine the axis of rotation for any hindered rotor. The proposed methods were applied to determine the torsional entropy of n- alkanes from ethane to hexane. The entropies calculated from the proposed methods give good agreement with the experimental and accurately calculated values and have a signi cantly better accuracy than the harmonic oscillator approximation. Furthermore, we performed approximate and full hindered rotor treatments to nd the corrected vibrational entropy of bis(chromiumtricarbonyl) dibenzo[a,e]cyclooctatetraene (DBCOT). The eighth chapter of this dissertation is an independent molecular dynamics (MD) project to study how ethanol interacts with human and mouse Toll-Like- Receptor3 (TLR3) monomers and a TLR3-dsRNA complex. No major structural changes were observed during the ethanol docking and subsequent MD simulations, but the MD simulations revealed a reduction in the proportion of alpha helix present during a 1000 ns MD simulation on the h-TLR3 monomer in 0.5 percent ethanol.

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This thesis is a product of the U.S. Army Corp of Engineer's desire to develop a more accurate procedure for estimating the load capacity of an in-service T-beam bridge. A bridge type that is a stumbling block for U.S. Army field engineers due to the unknown amount and placement of the flexural reinforcement in the T-beam girder cross-sections. Personnel from the U.S. Army Corp of Engineer's Waterways Experiment Station in cooperation with personnel from Virginia Tech conceived a procedure that is potentially more accurate, can be quickly executed in the field, and is relatively easy to use by field engineers. In general, the procedure provides a method for transition between the quantity of flexural reinforcement in a reinforced concrete T-beam and the member's actual moment of inertia. Specifically, the goal of this thesis is to evaluate the accuracy of selected, effective moment of inertia models as a component in the proposed analysis procedure. The accuracy of the selected models is evaluated with test data generated from a testing program detailed herein, which load tested full-scale reinforced concrete T-beams. The test specimens were subjected to a closely-spaced, tandem-axle load configuration, a load configuration typical of military equipment. / Master of Science

Abstract The studies of the deformed nucleus for the Pb isotopes in the A~190 re- gion has been carried out by using the P.S.M. The comparison between the theoretical calculation of the transition energy, kinetic moment of ine- rtia, dynamic moment of inertia, paring gap, rotational energy, quadrupole moment, and B(M1)/B(E2) and the experiment observations are presented. We found that the kinetic moment of inertia is increased as the spin incre- ase for the even-even nuclei. This rise has been interpreted as being due to the combined alignment of the quasiparticles in the high-N intruder or- bit. And the kinetic moment of inertia is constant function of spin in the odd-even nuclei. It is interpreted as been due to the Pauli blocking of odd -quasineutron in the high-N intruder orbit.

Unmanned Aerial Vehicles (UAV) control has become a very important point of scientific study. The control design challenges of a UAV make it one of the most researched areas in modern control applications. This thesis specifically chooses the Quadrotor as the UAV platform. Considering the quadrotor has 4 rotors and 6 degrees of freedom, it is an underactuated system and is dynamically unstable that has to be stabilized by a suitable control algorithm in order to operate autonomously. This thesis focuses on the quaternion representation of the quadrotor system dynamics and develops an adaptive control for its trajectory tracking problem. The control design uses the certainty equivalence principle where adaptive tracking controls are designed separately for each of the translational and rotational subsystems. With this approach, the success of the outer loop translational control relies on the fast convergence of the inner loop rotational control in order to guarantee the system’s stability while achieving the tracking objective. For the translational subsystem in the outer loop, a modified geometric control technique is considered with an adaptive component for the estimation of the uncertain mass of the quadrotor. For the rotational subsystem in the inner loop a backstepping based control design is adopted due to its systematic design and intuitive approach. An adaptive component is further integrated with it to estimate the integrated components of the uncertain Moment of Inertia matrix and other constant parameters in the system dynamics to guarantee the stability of the inner loop system while achieving the tracking objective. Furthermore, a complete backstepping control design methodology is presented which overcomes the issues of certainty equivalence principle where the inner loop needs to execute significantly faster than the outer loop to stabilize the system.

Muitas sÃo as ferramentas desenvolvidas para a resoluÃÃo de problemas de Geometria Euclidiana. O presente estudo apresenta uma ferramenta baseada no conceito fÃsico de centro de massa, proporcionando o desenvolvimento de habilidades necessÃrias na resoluÃÃo de problemas geomÃtricos, principalmente em relaÃÃo Ãs questÃes apresentadas em OlimpÃadas de MatemÃticas, tanto no Ensino Fundamental como no Ensino MÃdio. / There are many tools developed for solving Euclidean Geometry problems. This study presents a tool based on the physical concept of center of mass, allowing the development of the skills needed to solve geometric problems, especially the ones presented in Mathematics Olympiads, both in Elementary School and in High School.

The aim of the diploma thesis is to create a concept of methods that can be used for measurement of important mechanical inertia properties of bodies -- the coordinates of center of gravity and the the moment of inertia tensor, in case we don't have 3D model of these bodies. The thesis divides this problem into several sub-problems and suggests the solutions for each of them. Required equipment was created and measurement was carried out. At the end the measured values are compared with the teoretical ones and accuracy of this method is determined.

This thesis is the first part deals with methods of determining weight parameters of vehicles. By measuring the position of center of gravity and inertia measurements. In the second part focuses on the measurement of gravity position in a selected group of vehicles Škoda and their comparison between vehicles and comparison with simulation programs PCcrach and Virtual crach.

Road construction is important to make transports safe and sustainable. To compact asphalt an amount of energy needs to be conducted into the material either by static pressure or dynamic vibrations. An asphalt-roller compact the material and increases its load-bearing capacity. An eccentric shaft that generates vibrations is attached inside the roller drums. The shaft has two modes, varying between high eccentricity with slower pulses and low eccentricity with faster pulses. The study has been performed with the purpose to decrease the mass moment of inertia by redesigning the present eccentric shaft and verifying the new concepts with linear and non-linear FEM simulations. The new models were to have the same functional properties as the present eccentric shaft.  The current cross-section of the shaft was changed to a cross-section of a circle in the periphery. This was done by adding all features in new geometry to a simple shaft base and creating an analysis chain. To create the new lengthwise design brainstorming was used to generate ideas. The ideas were then sorted by using a Pugh matrix. CAD was used to model the concepts with the desired eccentric properties. Simulation in FEM software was used to acquire information about the behaviors during operation. Academic validation and useful information have been gathered by doing a literature review.  Two resulting concepts with properties fulfilling the prevailing restrictions. The circular cross-section in the periphery was adapted and the eccentric properties were kept. The simulation results from FEM software ended satisfactorily within limits for both execution in steel and ductile iron. For both concepts the mass moment of inertia was minimized, with 40.5 % in steel and in ductile iron with 42.0 % and 42.6 %.  An analysis chain has been performed showing that a cross-section with a circular geometry is optimal when the intention is to minimize the mass moment of inertia. It is possible to minimize the mass moment of inertia without negatively affecting the eccentric properties. The lengthwise design of a shaft with eccentric properties has been studied and simulated. Two concepts with varied lengthwise designs have been created with conserved eccentric properties and significantly decreased mass moment of inertia. The concepts can compose a good basis to continue investigating the lengthwise design which hopefully ends in a manufacturable eccentric shaft that contributes to environmental asphalt construction with low energy usage. / Tillverkning av vägar är viktigt för att transporter ska kunna utföras på ett säkert och hållbart sätt. För att packa asfalt behövs en mängd energi överföras till materialet genom statiskt tryck eller dynamiska vibrationer. En asfaltsvält packar materialet och ökar dess belastningsförmåga. En excentrisk axel som genererar vibrationer sitter inuti trummorna på välten. Denna axel har två lägen som varierar mellan att ha hög excentricitet med lägre puls samt låg excentricitet med högre puls.  Studien har genomförts med syftet att minska den nuvarande excenteraxelns masströghetsmoment genom att designa om den samt verifiera nya koncept med linjära och icke-linjära FEM beräkningar. De nya modellerna skulle behålla samma funktionella egenskaper som den nuvarande excenteraxeln. Det nuvarande tvärsnittet i XY-planet ändrades till en cirkel i rotationsaxlens periferi, genom att lägga till alla funktioner med nya tvärsnitt på en enkel axelbas i en analyskedja. En ny design i längsled påbörjades med brainstorming för att generera nya idéer. Idéerna sorterades sedan med hjälp av en Pugh-matris. Koncepten modellerades sedan med önskade excentriska egenskaper i CAD. FEM-mjukvara användes för att simulera koncepten och samla information om beteenden under körning. Akademisk validering och användbar information samlades in i en litteraturstudie.  Arbetet resulterade i två koncept med egenskaper som uppfyllde rådande krav. Det cirkulära tvärsnittet i periferin behölls och likaså de excentriska egenskaperna. FEM resultaten visade sig hamna tillfredsställande under gränserna med materialen stål och segjärn. För båda koncepten minskade masströghetsmomentet varav 40.5 % i stål och 42.0 % respektive 42.6 % i segjärn.  En analyskedja har genomförts som visat att ett tvärsnitt av en cirkel i periferi är optimalt med intentionen att minska masströghetsmomentet. Det är möjligt att minska masströghetsmomentet utan att påverka de excentriska egenskaperna negativt. Designen längs med en axel med excentriska egenskaper har studerats och simulerat. Två koncept med varierad design har modellerats, koncepten har behållna excentriska egenskaper och betydligt minskat masströghetsmoment. Koncepten kan utgöra gott underlag för fortsatt undersökning av designen i längdled. Förhoppningsvis kan det i sin tur resultera i en tillverkningsbar excentrisk axel som bidrar till miljövänligare asfaltskonstruktion med låg energiåtgång.

This thesis was made for EMBA Machinery AB and includes a product development process with the result of a concept model. EMBA is a company that develops and manufactures machines for the global corrugated board industry and wants to extend their solutions with a system that automatically removes the misprinted corrugated boards. The idea is to incorporate the system with the already existing processing flow and should be combined with the existing video system that validate the print quality. The concept model is a concept of the mechanical parts needed for the solution and can be used as a foundation for further work towards a product for the market. To produce this concept model methods for divergent problem solving were used. Several concept solutions were created and evaluated with the purpose of finding the best one. This concept was then developed further into a 3D-model of all the interlocking machine- and construction elements, whom in detail demonstrates the removal of misprinted boards. Calculations, which included determining moment of inertia and an acceleration curve, were also done based on data from this model with the intent of testing the plausibility of the solution and to offer a theoretical foundation on which to base further work with this concept. / Det här examensarbetet utfördes åt EMBA Machinery AB och innefattar en produktutvecklingsprocess med slutresultat i en konceptmodell. Företaget utvecklar och tillverkar i dag maskiner för den globala wellpapp-industrin och önskar nu komplettera sitt utbud med ett system som automatiskt sorterar bort wellpappark som erhållit felaktigt grafiskt tryck. Detta är tänkt att kunna inkorporeras i deras befintliga processeringsflöde och skall kombineras med befintlig videoteknik för validering av det grafiska trycket. Konceptmodellen som tas fram är således en potentiell lösning av de mekaniska delar som samverkar i sållningen av feltryckta ark och är tänkt som en grund för vidare arbete att ta fram en marknadsfärdig produkt. I processen att ta fram denna konceptmodell tillämpades metoder för divergent problemlösning där flera lösningskoncept genererades och värderades i syfte att hitta det bästa. Detta koncept utvecklades sedan till en mer detaljerad representation av lösningen i form av en 3D-modell av de samverkande maskin- och konstruktionselementen, vilken i detalj demonstrerar hur det valda konceptet löser sållningen av feltryckta ark. Beräkningar, vilka innefattade framtagning av tröghetsmoment och accelerationskurva, utfördes även med data från denna modell i syfte att testa lösningens rimlighet och att erbjuda en teoretisk grund att jobba vidare med i fortsatt arbete av konceptet.