10 ENGLISH BOOKS RELATING TO «TAUTOCHRONISM»
Discover the use of
tautochronism in the following bibliographical selection. Books relating to
tautochronism and brief extracts from same to provide context of its use in English literature.
1
Proceedings of the Section of Sciences
Tautochronism. The condition that a motion along a given curve I >o
tautochronous is: the tangential component of the force must be proportional to
the length of the arc between the moving point to a point of (he curve; in that case
the motion ...
2
Proceedings of the Koninklijke Nederlandse Akademie Van ...
Tautochronism. The condition that a motion along a given curve be
tautochronous is: the tangential component of the force must be proportional to
the length of the arc between the moving point to a point of the curve; in that case
the motion ...
Koninklijke Akademie van Wetenschappen (Netherlands). Afdeeling Natuurkunde, 1904
3
The Mathematical and Other Writings of R. L. E. ... Edited ...
0 and the necessary and sufficient condition of tautochronism is a” = Aw. Hence
generally 1'11 dz 0 N/le—Fz is independent of 2', provided z' = A . Fz. Now, when
R = kv', there is win it ,—_ _ $"“" 9013' therefore eflv' = — 29]. e'“ g: da. do: L t :f ...
Robert Leslie Ellis, 1863
4
A treatise on infinitesimal calculus: containing ...
Some examples of tautochronism are subjoined. Ex. 1. Let the impressed velocity
-increment be that of gravity ; and let us suppose the axes of coordinates and
origin to be taken so that the axis of x is vertical, and * = 0 when x = 0 ; then , ax T
...
5
Optics and Spectroscopy
Design of achromatic hologram lens systems using the principle of tautochronism
of rays K. S. Mustafin (Submitted 23 March 1977) Opt. Spektrosk. 44, 164-167 (
January 1978) A simple method of designing and constructing achromatic ...
6
The Cambridge Mathematical Journal
dx therefore e •** v* = — /<fr e-*K* ^ ds, o therefore e~2is«2 = 2g (/*, — /*), o Put
rfz = «-*s rfs> and let « and s be equal to zero together, therefore z — - (1 — e~ts)
, /s = Fz, ft. 2, — FZ 0 Therefore for tautochronism z2 = A.Fz. But Fz = / — (1 — kz)
...
Duncan Farquharson Gregory, Robert Leslie Ellis, 1841
7
The Cambridge and Dublin Mathematical Journal
... the resistance is equal to kv* or to hv -f kv1, to the cases in which it is a cycloid,
viz. when the resistance is equal to zero or to hv. In vacuo », '** ^/v^' and the
necessary and sufficient condition of tautochronism is *s = Ax. Hence generally
dz ...
8
Dynamics, or a treatise on motion; to which is added a short ...
(3) be expanded (if necessary) and arranged in powers of k, the condition of
tautochronism will be that the equation must be satisfied for all values of k, and
therefore the coefficients of the different powers of k must be separately equal to
zero.
9
The elementary part of A treatise on the dynamics of a ...
By deducing the condition of tautochronism from Lagrange's expression we
prove that it is sufficient, the mode of proof adopted above shows that the
condition is also necessary. 496. Ex. 1. Euler's theorem. A particle moves on a
smooth curve ...
10
The Cambridge Mathematical Journal
In vacuo », s/2gtl = \j-L — , 1 J Vxt — x 0 and the necessary and sufficient
condition of tautochronism is sa = Ax. Hence generally /, dz Vfzl — Fz b is
independent of zv provided z2 = A.Fz. Now, when R = kv1, there is d.vdv . „ dx ...
