What is d'Alembert's Principle?
This post is really more to do with
statics, surprisingly, and concerns a way of tackling dynamics
problems that was devised by a French scientist called d’Alembert.
At the time of its introduction it was very difficult to understand
but nowadays we are all familiar with some of its applications in
space travel.
Suppose we consider the case of
astronauts being launched into space on a space shuttle. During the
launch when the shuttle is vertical and accelerating rapidly up
through the atmosphere with the rockets at full blast, the astronauts
feel as though they have suddenly become extremely heavy; they cannot
raise their arms from the arms of the seat, they cannot raise their
heads from the headrests and the skin on their faces is pulled back
tight because it is apparently so heavy.
We know that all this is because the
shuttle is accelerating so fast that the astronauts are subjected to
what are known as ‘g-forces’, the sort of forces you feel on a
roller coaster as it goes through the bottom of a tight curve.
However, if you were in the space
shuttle and the windows were blacked out so that you could not see
any movement, you could be excused for thinking that the astronauts
really were being subjected to some large extra force acting in the
opposite direction to the acceleration.
For an astronaut of mass m experiencing
an acceleration of a directly upwards, the extra imaginary force
would be F = ma directly down, according to Newton’s second law.
From that point on, any engineering dynamics problem concerning the
astronaut, such as working out the reaction loads on the seat anchor
points, could be carried out as a statics calculation with this
imaginary force included.
This is d’Alembert’s principle.
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