Thesis (Ph. D.)--University of Washington, 2000. / Vita. Includes bibliographical references (leaves 94-96).

This thesis studies the dynamics and stability of some bicycles. The dynamics of idealized bicycles is of interest due to complexities associated with the behaviour of this seemingly simple machine. It is also useful as it can be a starting point for analysis of more complicated systems, such as motorcycles with suspensions, frame flexibility and thick tyres. Finally, accurate and reliable analyses of bicycles can provide benchmarks for checking the correctness of general multibody dynamics codes. The first part of the thesis deals with the derivation of fully nonlinear differential equations of motion for a bicycle. Lagrange’s equations are derived along with the constraint equations in an algorithmic way using computer algebra.Then equivalent equations are obtained numerically using a Newton-Euler formulation. The Newton-Euler formulation is less straightforward than the Lagrangian one and it requires the solution of a bigger system of linear equations in the unknowns. However, it is computationally faster because it has been implemented numerically, unlike Lagrange’s equations which involve long analytical expressions that need to be transferred to a numerical computing environment before being integrated. The two sets of equations are validated against each other using consistent initial conditions. The match obtained is, expectedly, very accurate. The second part of the thesis discusses the linearization of the full nonlinear equations of motion. Lagrange’s equations have been used.The equations are linearized and the corresponding eigenvalue problem studied. The eigenvalues are plotted as functions of the forward speed ν of the bicycle. Several eigenmodes, like weave, capsize, and a stable mode called caster, have been identified along with the speed intervals where they are dominant. The results obtained, for certain parameter values, are in complete numerical agreement with those obtained by other independent researchers, and further validate the equations of motion. The bicycle with these parameters is called the benchmark bicycle. The third part of the thesis makes a detailed and comprehensive study of hands-free circular motions of the benchmark bicycle. Various one-parameter families of circular motions have been identified. Three distinct families exist: (1)A handlebar-forward family, starting from capsize bifurcation off straight-line motion, and ending in an unstable static equilibrium with the frame perfectly upright, and the front wheel almost perpendicular. (2) A handlebar-reversed family, starting again from capsize bifurcation, but ending with the front wheel again steered straight, the bicycle spinning infinitely fast in small circles while lying flat in the ground plane. (3) Lastly, a family joining a similar flat spinning motion (with handlebar forward), to a handlebar-reversed limit, circling in dynamic balance at infinite speed, with the frame near upright and the front wheel almost perpendicular; the transition between handlebar forward and reversed is through moderate-speed circular pivoting with the rear wheel not rotating, and the bicycle virtually upright. In the fourth part of this thesis, some of the parameters (both geometrical and inertial) for the benchmark bicycle have been changed and the resulting different bicycles and their circular motions studied showing other families of circular motions. Finally, some of the circular motions have been examined, numerically and analytically, for stability.

Currently, two methods exist to determine trajectory of a ballistic penetrator: Poncelet Analysis and Differential Area Force Law (DAFL) methods. An exact solution for the Poncelet Equation exists; making for easy computation. However, the one dimensional nature of the equation fails to capture the intricate three-dimensional nature of real world ballistic penetrator trajectories. The DAFL methods employ empirically derived stress algorithms to calculate to forces acting on a differential area of a projectile. These stresses are then used to determine the forces and moments acting on the differential areas. These forces and moments are then used to solve the equations of motion to determine the trajectory of the ballistic penetrator. The DAFL methods accurately capture the three dimensional nature of the penetrator's trajectory, but are computationally intensive which make them slow. The Integrated Force Law (IFL) method combines the computational ease of the Poncelet Analysis with the accuracy of the DAFL methods. In IFL, the projectile shape is modeled as a polynomial. The stress algorithms used in the DAFL methods are them numerically integrated over the top and bottom surfaces of the projectile to determine the force and moment acting on the top and bottom half of the weapon. These two forces and moments are then used to solve the equations of motion. J-hook trajectories are solved in less than 40 seconds and stable trajectories are solved in less than three seconds.

As equações de movimento de uma partícula (nucleon) interagindo com um campo escalar (mesônico) são obtidas pelo método dos momentos do tensor energia-momentum, de Papapetrou. Depois de um estudo detalhado do campo de radiação mesônico estabelecemos a expressão da força de reação de radiação do campo sobre a partícula. / The equations of motion of a particle (nucleon) interacting with a scalar (mesonic) field are derived by the energy-momentum tensor moments method of Papapetrou. After a detailed study of the mesonic radiation field we establish an expression of the reactive radiation force on the field upon the particle.

Thèse : Sciences mathématiques : Paris, Faculté des sciences : 1854. / Thèse de mécanique : Mouvement dans un milieu résistant d'un point matériel attiré par un centre fixe, p. [3]-34. Thèse d'astronomie : De la figure de l'anneau de Saturne, p. [35]-52. Titre provenant de l'écran- titre.

Thèse : Sciences : Paris : 1855. / Thèse d'astronomie, 78 p. at end, has title: Application de la méthode de M.-Hamilton au calcul des perturbations de Jupiter. Titre provenant de l'écran-titre.

Thesis (Ph. D.)--University of Washington, 2002. / Vita. Includes bibliographical references (leaves 130-134).

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Thesis (Ph.D.) - University of Queensland, 2003. / Includes bibliography.

As equações de movimento de uma partícula (nucleon) interagindo com um campo escalar (mesônico) são obtidas pelo método dos momentos do tensor energia-momentum, de Papapetrou. Depois de um estudo detalhado do campo de radiação mesônico estabelecemos a expressão da força de reação de radiação do campo sobre a partícula. / The equations of motion of a particle (nucleon) interacting with a scalar (mesonic) field are derived by the energy-momentum tensor moments method of Papapetrou. After a detailed study of the mesonic radiation field we establish an expression of the reactive radiation force on the field upon the particle.