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1
The Elementary Part of a Treatise on the Dynamics of a ...
That a smooth cyoloid is tautochronous in vacuo for a heavy particle was first
proved by Huygens in his Horologium Oscillatorium, 1673. Newton extended this
to the case in which the resistance is 2kv, and also proved that a smooth
epicycloid ...
2
A Treatise on the Dynamics of a System of Rigid Bodies ...: ...
That a smooth cycloid is tautochronous in vacuo for a heavy particle was first
proved by Huygens in his Horologium Oscillatorium, 1673. Newton extended this
to the case in which the resistance is 2kv, and also proved that a smooth
epicycloid ...
3
Elementary Rigid Dynamics
The tautochronous arcs terminate at the point given by F = O and the period is -zr/
2m. 494:. That cycloidal oscillations in a medium in which the resistance varies
as the velocity are tautochronous has been proved by Newton in the second ...
7.2, rather than a circular track, its motion will be perfectly tautochronous (under
the constant gravity field of the earth). The radius of curvature of the cycloid near
the point O is 4a, hence one understands why the complete period of oscillation ...
5
A Treatise On Dynamics Of A Particle
If the resistance vary as the square of the velocity, the motion is discussed in Art.
129. 211. Tautochronous curves. When a particle oscillates on a given smooth
curve either in a vacuum or in a medium whose resistance varies as the velocity,
...
6
Science Teaching: The Role of History and Philosophy of Science
theoretical object, namely the claims that period varied with length, and that the
circle was the tautochronous curve (the curve on which bodies falling freely
under the influence of gravity reach the nadir at the same time regardless of
where ...
Michael R. Matthews, 1994
7
A Treatise on Dynamics. Containing a ... collection of ...
If a body move upon a curve, the curve is said to be tautochronous, if the time of
descent to a given point he the same, from whatever point the body begin to
descend. We shall consider the body as descending to the lowest point. ' PROP.
8
On the motion of points constrained and resisted, and on the ...
Ill, Tautochronous Curves. 166. If a body move upon a curve, the curve is said to
be tautochronous, if the time of descent to a given point be the same, from
whatever point the body begin to descend. We shall consider the body as
descending ...
9
A Treatise on Dynamics: Containing a Considerable Collection ...
Tautochronous Curves. 45. If a body move upon a curve, the curve is said to be
tautochronous, if the time of descent ... When a body is acted upon by a constant
force in parallel lines, to find the tautochronous curve. Let A, fig. 59, be the lowest
...
10
The Mathematical Principles of Mechanical Philosophy: And ...
X This expression is independent of h and therefore points out the remarkable
fact that however large the arc of vibration be the time of oscillation is the same in
all. For this reason the cycloid is called a Tautochronous Curve. * Prop. A particle
...
