JosephLouis
Lagrange not
only provided
brilliant
analyses
which were
eventually
to facilitate,
among other
things,
modernday
satellites,
but reveled
in and
put on
display
the sheer
beauty
of mathematics.
One of
Lagrange's
works,
Mécanique
Analytique,
has been
described
as a "scientific
poem".
Lagrange's
image is
inscribed
with the "EulerLagrange
equation",
a seminal
differential
equation
in the
'calculus
of variations',
which concerns
itself
with paths,
curves,
and surfaces
for which
a given
function
has a stationary
value.
Lagrange's
portrait shares
a color
palette
with
other
pioneers
of calculus,
including Newton, Leibniz,
and Laplace,
Lagrange's
image is
backed
by a color
plot of
fields
surrounding
points
in space,
overlaid
by a triangle
identifying
and connecting
3 critical
"Lagrangian
points",
named after
Lagrange
who first
showed
their existence.
These
3 Lagrangian
points
define
a position
in space
where
the pulls
of two
rotating
gravitational
bodies
(such
as the
EarthMoon,
or Earthsun)
combine
to form
a point
at which
a third
body
of comparatively
negligible
mass
would
remain
stationary
relative
to the
two bodies.
Lagrangian
points have proven
invaluable
in positioning
satellites
for synchronous
orbit,
and more
recently,
other Lagrangian
points
first thought
unstable,
have
become the basis for 'chaotic control'. This is a
relatively
new technique
being explored
for space
flight,
similar
to gravity
assist,
which may
enable
practical
interplanetary
missions
 flown
with much
smaller
amounts
of fuel.
