A time-discrete formulation of the variational principle of mechanics is used to provide a consistent theoretical framework for the construction and analysis of low order integration methods. These are applied to mechanical systems subject to mixed constraints and dry frictional contacts and impacts---machines. The framework includes physics motivated constraint regularization and stabilization schemes. This is done by adding potential energy and Rayleigh dissipation terms in the Lagrangian formulation used throughout. These terms explicitly depend on the value of the Lagrange multipliers enforcing constraints. Having finite energy, the multipliers are thus massless ghost particles. The main numerical stepping method produced with the framework is called SPOOK. Variational integrators preserve physical invariants globally, exactly in some cases, approximately but within fixed global bounds for others. This allows to product realistic physical trajectories even with the low order methods. These are needed in the solution of nonsmooth problems such as dry frictional contacts and in addition, they are computationally inexpensive. The combination of strong stability, low order, and the global preservation of invariants allows for large integration time steps, but without loosing accuracy on the important and visible physical quantities. SPOOK is thus well-suited for interactive simulations, such as those commonly used in virtual environment applications, because it is fast, stable, and faithful to the physics. New results include a stable discretization of highly oscillatory terms of constraint regularization; a linearly stable constraint stabilization scheme based on ghost potential and Rayleigh dissipation terms; a single-step, strictly dissipative, approximate impact model; a quasi-linear complementarity formulation of dry friction that is isotropic and solvable for any nonnegative value of friction coefficients; an analysis of a splitting scheme to solve frictional contact complementarity problems; a stable, quaternion-based rigid body stepping scheme and a stable linear approximation thereof. SPOOK includes all these elements. It is linearly implicit and linearly stable, it requires the solution of either one linear system of equations of one mixed linear complementarity problem per regular time step, and two of the same when an impact condition is detected. The changes in energy caused by constraints, impacts, and dry friction, are all shown to be strictly dissipative in comparison with the free system. Since all regularization and stabilization parameters are introduced in the physics, they map directly onto physical properties and thus allow modeling of a variety of phenomena, such as constraint compliance, for instance. Tutorial material is included for continuous and discrete-time analytic mechanics, quaternion algebra, complementarity problems, rigid body dynamics, constraint kinematics, and special topics in numerical linear algebra needed in the solution of the stepping equations of SPOOK. The qualitative and quantitative aspects of SPOOK are demonstrated by comparison with a variety of standard techniques on well known test cases which are analyzed in details. SPOOK compares favorably for all these examples. In particular, it handles ill-posed and degenerate problems seamlessly and systematically. An implementation suitable for large scale performance and accuracy testing is left for future work.

Loads determination for external stores on fighter aircraft is an important task for manufacturers in ensuring the safe operation of their aircraft. Due to the large number of possible store combinations, wind tunnel tests – the primary approach to obtaining loads data – cannot be performed for all configurations. Instead, supplementary techniques to estimating loads are necessary. One approach is to use information from another store and adapt it, using so-called scaling methods, to the non-tested store. In this thesis, a scaling method combining the results of computational fluid dynamics (CFD) simulations, for both a non-tested and a reference store, with existing wind tunnel data for the reference store, is thoroughly examined for a number of different stores, angles of attack, sideslip angles and Mach numbers. The performance of the proposed scaling method is assessed in relation to currently used scaling methods, using non-parametric and multivariate statistics. The results show no definitive improvement in performance for the proposed scaling method over the current methods. Although the proposed method is slightly more conservative, considerable variability in the estimates and an increased time consumption for scaling leads the author to advise against using the proposed method for scaling aerodynamic loads on external stores. / Lastbestämning för yttre utrustning på stridsflygplan är en viktig uppgift för att tillverkarna ska kunna garantera säkerheten för sina flygplan. Då antalet möjliga utrustningskombinationer är mycket stort, kan inte vindtunneltester – normalt den främsta metoden för att erhålla lastdata – utföras för alla konfigurationer. Således behövs kompletterande metoder för att skatta laster. Ett alternativ är att använda data från en annan utrustning och anpassa den, med hjälp av så kallade skalningsmetoder, till den icke-testade utrustningen. I detta examensarbete behandlas en skalningsmetod som kombinerar resultaten från numeriska strömningsberäkningar – så kallade CFD-simuleringar – för både en testad och en icke-testad utrustning med befintliga vindtunneldata för den testade utrustningen. Metoden undersöks grundligt för ett antal olika utrustningar, anfallsvinklar, sidanblåsningsvinklar och Machtal. Prestandan hos den föreslagna skalningsmetoden utvärderas i relation till nu använda skalningsmetoder, baserat på icke-parametrisk och multivariat statistik. Resultaten visar inga definitiva förbättringar av prestanda för den föreslagna skalningsmetoden jämfört med de nuvarande metoderna. Även om den föreslagna metoden är något mer konservativ, så föranleder betydande variationer i skattningar och en ökad tidsåtgång för skalning författaren att avråda från att använda den föreslagna metoden för skalning av luftlaster på yttre utrustning.