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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Archives of orthopaedic and trauma surgery 110 (1990), S. 1-14 
    ISSN: 1434-3916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Summary To investigate the expectation of general insufficiency of osteoblasts with increasing age, we studied autotopsy material from 105 deceased persons of both sexes who had died between 16 and 91 years and in whom clinically manifest diseases of the bone had been excluded. Quantitative morphometric examination of the structure of the spongy bone of the 3rd–5th lumbar vertebral bodies (LVBs) and of the 5th–7th cervical vertebral bodies (CVBs) was carried out in frontal and saggital planes, the parameters analysed being volumetric density (Vv), surface density (Sv) and specific surface area (S/V), and the results were subjected to statistical evaluation. The results showed that in the three LVBs, Vv, Sv and S/V behave in a similar manner, Vv and Sv decreasing after the age of 50 years by more than one-third while S/V remains constant throughout life. The three lower CVBs had higher values than the LVBs for all three structural parameters. In the 7th CVB somewhat lower Vv and Sv values and higher S/V values were found than in the 5th and 6th. The age-related changes, by contrast, were very small. This differing behavior of the spongy bone in the two regions of the spinal column is an expression of the different characteristic loading forces in each regions: LVB loading is predominantly static, CVB loading mainly dynamic. Thus, from the functional point of view, what is known as “physiological osteoporosis due to ageing” is nothing more than adaptation by an ageing bone to physical activity, reflecting —like the bone of the young adult — the current loading of the cancellous bone by the actions of the musculoskeletal system. Since such physical activity is often age-related, the performance of the osteoblasts does not depend upon age per se, but merely on the remaining functional adaptive capacities of the ageing organism as whole.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 78 (1993), S. 443-463 
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion games ; open-loop strategies ; multiple shooting ; multipoint boundary-value problems ; saddle-point trajectories ; barrier trajectories ; missile firing range
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Part 1 of this paper (Ref. 1), necessary conditions for optimal open-loop strategies in differential games of pursuit-evasion type have been developed for problems which involve state variable inequality constraints and nonsmooth data. These necessary conditions lead to multipoint boundary-value problems with jump conditions. These problems can be solved very efficiently and accurately by the well-known multiple-shooting method. By this approach, optimal open-loop strategies and their associated saddle-point trajectories can be computed for the entire capture zone of the game. This also includes the computation of optimal open-loop strategies and saddle-point trajectories on the barrier of the pursuit-evasion game. The open-loop strategies provide an open-loop representation of the optimal feedback strategies. Numerical results are obtained for a special air combat scenario between one medium-range air-to-air missile and one high-performance aircraft in a vertical plane. A dynamic pressure limit for the aircraft imposes a state variable inequality constraint of the first order. Special emphasis is laid on realistic approximations of the lift, drag, and thrust of both vehicles and the atmospheric data. In particular, saddle-point trajectories on the barrier are computed and discussed. Submanifolds of the barrier which separate the initial values of the capture zone from those of the escape zone are computed for two representative launch positions of the missible. By this way, the firing range of the pursuing missile is determined and visualized.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 78 (1993), S. 419-441 
    ISSN: 1573-2878
    Keywords: Differential games ; pursuit-evasion games ; singular surfaces ; barrier surface ; state constraints ; open-loop strategies ; multipoint boundary-value problems ; flight mechanics ; missile firing range
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 67 (1990), S. 421-435 
    ISSN: 1573-2878
    Keywords: Neighboring extremals ; accessory minimum problem ; feedback controls ; closed-loop controls ; inequality constraints ; multiple shooting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A very fast numerical method is developed for the computation of neighboring optimum feedback controls. This method is applicable to a general class of optimal control problems (for example, problems including inequality constraints and discontinuities) and needs no on-line computation, except for one matrix-vector multiplication. The method is based on the so-called accessory minimum problem. The necessary conditions for this auxiliary optimal control problem form a linear multipoint boundary-value problem with linear jump conditions, which is especially well suited for numerical treatment. In the second part of this paper, the performance of the guidance scheme is shown for the heating-constrained cross-range maximization problem of a space-shuttle-orbiter-type vehicle.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    Springer
    Journal of optimization theory and applications 67 (1990), S. 437-446 
    ISSN: 1573-2878
    Keywords: Neighboring extremals ; accessory minimum problem ; feedback controls ; neighboring optimum guidance ; multiple shooting ; guidance of space vehicles ; space shuttle
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The application and the performance of the neighboring optimal feedback scheme presented in Part 1 of this paper is demonstrated for the heating-constrained cross-range maximization problem of a space-shuttle-orbiter-type vehicle. This problem contains five state variables, two control variables, and a state variable inequality constraint of order zero.
    Type of Medium: Electronic Resource
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