Eich, E. "Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten." PhD, University of Augsburg (1991).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be solved by Newton iteration. For an introduction to BDF methods see [6, 7, 8] However, substituting the true values fy(t i )g for fe y i g in (11) and Y k;n 1 (t n 1 ) we merely note that the local truncation error n 1 b Y k;n 1 (t n 1 ) f(t n 1 ; e y(t n 1 ) n 1 7 may be written [1, 5] n 1 = h Delta n 1 (t n 1 ) Delta y[t n 1 ; t n ; t n 1 Gammak ] where y[t n 1 ; t n . t n 1 Gammak ] is the Newton divided difference computed from the values fe y n 1 ; e y n ; e y n 1 Gammak g and n 1 (t) t Gamma t n 1 Gammal ) which thus implies n 1 ....

Eich, E. "Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten." PhD, University of Augsburg (1991).

....of suitable orders and stepsizes is non trivial and has been the subject of much research. Given suitable methods to compute and advance the integration formulae, it can make the difference between a good and a bad code. A number of different approaches have been suggested for this problem [1, 2, 4, 5, 8, 9, 10, 11]. This work concentrates on and extends two of these: one implemented by Shampine in his code RDEAM [11] and a second, simpler, version based on the difference between a predictor and corrector formula. Communicated by Prof. C. T. H. Baker, this document originally appeared as an IWR preprint ....

....By retaining the notation and the variables of schemes used to advance the integration, the broader mathematical context is lost. The dependence of h is spread in a complicated way throughout several terms and extensive manipulation and assumptions are needed to make even the smallest advances [1, 4, 9]. Confronted with this problem, it is natural to take one step back. Recurrence relations (c.f. for g k 1;1 and g k;1 ) rescaling ratios (fi k 1 ) and heuristics are clearly important for the practical implementation of numerical codes but distract from the basic principles underlying their ....

Eich, E. "Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten." PhD, University of Augsburg (1991).

....by Newton iteration. For an introduction to BDF methods see [6, 7, 8] However, substituting the true values fy(t i )g for fe y i g in (11) and Y 0 k;n 1 (t n 1 ) we merely note that the local truncation error n 1 b Y 0 k;n 1 (t n 1 ) f(t n 1 ; e y(t n 1 ) n 1 7 may be written [1, 5] n 1 = h Delta 0 n 1 (t n 1 ) Delta y[t n 1 ; t n ; t n 1 Gammak ] where y[t n 1 ; t n . t n 1 Gammak ] is the Newton divided difference computed from the values fe y n 1 ; e y n ; e y n 1 Gammak g and n 1 (t) k Y l=0 (t Gamma t n 1 Gammal ) which thus ....

Eich, E. "Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten." PhD, University of Augsburg (1991).

....the back of the wheel and the check rail of the switch. Table 1 shows the different normal contact models. The inequality 0 means that the value of each constraint force at the wheel rail interface is sampled after every successful integration step by means of the root function technique, [20]. Wheel lift ( indicated by = 0 ) may be caused by a hard running of the wheel at the check rail or due to hollow worn wheel running through the common crossing. In this case the constraint is skipped and the normal contact is treated as flexible further on. wheel rail interconnection: ....

Eich, E. (1992) "Projizierende Mehrschrittverfahren zur numerischen Losung der Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten " VDI--Verlag, Dusseldorf, Fortschritt-Berichte VDI Reihe 18, Nr. 109, 1992.

....least when taking one single step. This approach also offers the chance to obtain errorcontrolled results, if the interpolation routines of the integrators are natural. Also, it is usually much faster and more efficient than hoping for the integrators to stumble, but not trip over discontinuities ([6], 17] Furthermore, if there are jump discontinuities in the model, model validation is impossible without localizing the exact time of occurrence of the discontinuity. 5.3.1 State Event Finder (SEF) For these reasons, all the integrators in MBSSIM have a SEF built in. This is an ....

....the model, model validation is impossible without localizing the exact time of occurrence of the discontinuity. 5.3.1 State Event Finder (SEF) For these reasons, all the integrators in MBSSIM have a SEF built in. This is an implementation of the safeguarded root finding algorithm described in [6] and it will search for the roots of the switching functions iteratively. The switching functions themselves are assumed to be of the form q(t; s; s; p; p; v; v) 0 : Although by evaluating the parts of the model equations and solving the resulting linear system, one could equivalently ....

[Article contains additional citation context not shown here]

E. Eich. Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten, Dissertation, Universitat Augsburg, Augsburg, 1991.

....e.g. incorporating the Dwell time and the Dahl effect. Most of these additional effects can be easily added to the model described below, if necessary. In the literature, friction is usually modeled by three valued logic (sliding forward, sliding backward, stuck) see e.g. Cellier 1979, Eich 1992). In (Elmqvist et al. 1993, Otter 1994) it is shown, that 5 switching states are needed, if more than one discontinuous element is present (e.g. several friction elements) The two additional switching states describe the sliding begin, when the relative velocity is still zero. Contrary to a ....

Eich E. 1992. "Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten." VDI-Fortschritt-Berichte, Reihe 18, Nr. 109, VDI-Verlag, Dusseldorf.

....of suitable orders and stepsizes is non trivial and has been the subject of much research. Given suitable methods to compute and advance the integration formulae, it can make the difference between a good and a bad code. A number of different approaches have been suggested for this problem [1, 2, 4, 5, 8, 9, 10, 11]. This work concentrates on and extends two of these: one implemented by Shampine in his code RDEAM [11] and a second, simpler, version based on the difference between a predictor and corrector formula. Communicated by Prof. C. T. H. Baker, this document originally appeared as an IWR preprint ....

....By retaining the notation and the variables of schemes used to advance the integration, the broader mathematical context is lost. The dependence of h is spread in a complicated way throughout several terms and extensive manipulation and assumptions are needed to make even the smallest advances [1, 4, 9]. Confronted with this problem, it is natural to take one step back. Recurrence relations (c.f. for g k 1;1 and g k;1 ) rescaling ratios (fi k 1 ) and heuristics are clearly important for the practical implementation of numerical codes but distract from the basic principles underlying their ....

Eich, E. "Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten." PhD, University of Augsburg (1991).

.... if fi = 0; 23) where fi is the rotor velocity, T is the rotor torque, fi) models the velocity dependence of friction, and 0 = 0) The complicated nature of friction introduces state dependent discontinuities in the dynamic equations, requiring proper numerical treatment by switching functions [18, 58, 61]. Furthermore, dry friction may cause rank deficiencies in the optimization problem. Numerical investigations of optimal robot trajectories under the influence of friction have been performed in [22] where a Coulomb friction model is used, that is, fi) j 0 in (23) More generally, the velocity ....

E. Eich. Projizierende Mehrschrittverfahren zur numerischen L osung von Bewegungsgleichungen technischer Mehrk orpersysteme mit Zwangsbedingungen und Unstetigkeiten. Number 109 in Fortschr.-Ber. VDI, Reihe 18: Mechanik/Bruchmechanik. VDI Verlag, D usseldorf, 1991.

No context found.

Eich, E.: Projizierende Mehrschrittverfahren zur numerischen Losung von Bewegungsgleichungen technischer Mehrkorpersysteme mit Zwangsbedingungen und Unstetigkeiten. Fortschritt-Berichte VDI, Reihe 18, Nr. 109 (Dusseldorf: VDI-Verlag, 1992)

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