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Mappings preserving some distances

Billich M.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2008

Vol. 13

10-14

We deal with mappings which preserve unit (some positive) distance, as well as with mappings contracting (expanding) some distance. In particular, we show that a mapping preserving three positive distances is an isometry.

Drgania własne regularnego układu o "n" stopniach swobody w ujęciu analitycznym

Palej R., Goik T.

Zeszyty Naukowe Politechniki Rzeszowskiej. Mechanika

2002

z. 60 [197]

465-472

The paper deals with the free vibrations of damped multi-degree-of-freedom-systems. The criterion of critical damping as well as the total number of damping cases are discussed. The analytical solutions for chosen cases are presented. General considerations have been illustrated by a numerical example where time response of a 50-degree-of-freedom-system to a velocity jump of the end mass is presented.