A Treatise on the Theory of Screws
Forfatter: Sir Robert Stawell Ball
År: 1900
Forlag: The University Press
Sted: Cambride
Sider: 544
UDK: 531.1
Søgning i bogen
Den bedste måde at søge i bogen er ved at downloade PDF'en og søge i den.
Derved får du fremhævet ordene visuelt direkte på billedet af siden.
Digitaliseret bog
Bogens tekst er maskinlæst, så der kan være en del fejl og mangler.
516
THE THEORY OF SCREWS.
(0, 0), (0, 1) ...
(1, 0), (1, 1) ...
* We may remark that since the moment of two lines is the virtual coefficient of two screws
of zero pitch, these equations are given at once by virtual velocities, if we rotate the body round
each of the forces in succession.
Spottiswoode (W.)—Note sur Véquilibre des forces dans Vespace. Comptes
Rendus; Vol. Ixvi., pp. 97-103 (January, 1868).
If P^... Pn_^ be n forces in equilibrium, and if (0, 1) denote the moment of
Po, P1, then the author proves* that
A(0, l) + A.(0, 2) + ...=0,
p, (1,0)+ + P2 (1, 2) + ... = 0,
Po(2, 0) + P1(2, 1)+ +...=0.
As we have thus n equations to determine only the relative values of n quantities,
the redundancy is taken advantage of to prove that
p 2 p 2
[0, 0] “ [1,
where [0, 0], [1, 1], &c., are the coefficients of (0, 0), (1, 1), &c., in the determinant
He then considers the quaternion q = — @, already mentioned (p. 512), and
introduces the new quaternion Q = = c + y. The scalar c (the pitch) is inde-
pendent of the assumed origin, and the vector y is the vector to a definite point C
on the central axis. This point does not vary with the position of the assumed
origin, and is called the “Centre of the System of Forces.” When the forces are
all parallel G coincides with the centre of the parallel forces. In general
Ttaß = V(c2 + 7’/) Ttß,
or the tensor of the total moment is constant for all points 0 situated on a sphere
whose centre is C, and becomes a minimum when 0 coincides with C.
In Art. 396 Hamilton says “ the passage of a right line from any one given
position in space to any other maybe conceived to be accomplished by a sort of screw
motion," and on these kinematical lines he worked out his theory of the “Surface of
Emanants,” generated by a line moving according to some given law and constantly
intersecting a given curve in space.
Plücker (J.)—Fundamental views regarding mechanics. Phil. Trans. (1866); Vol.
clvi., pp. 361—380.
The object of this paper is to “ connect, in mechanics, translatory and rotatory
movements with each other by a principle in geometry analogous to that of re-
ciprocity.” One of the principal theorems is thus enunciated:—“Any number of
rotatory forces acting simultaneously, the co-ordinates of the resulting rotatory
force, if there is such a force, if there is not, the co-ordinates of the resulting
rotatory dyname, are obtained by adding the co-ordinates of the given rotatory
forces. In the case of equilibrium the six sums obtained are equal to zero.”