System
To model and analyze a dynamical system, we will use a bicycle as our
model. There are two gears and a chain involved in the foot action or
forces acted on the foot pedals. The foot action force translates the
motion to the back wheel and later to the front wheels.
In order to be able
to analyze the bicycle in terms of the translational mechanical system,
we must first state that the input force is the foot action. We are
assuming that the chain is an ideal chain. The chain is losing no energy
when transferring the force from the first gear to the second gear.
The force is then translated to the wheel through the axle, which is
attached to the second gear and tire. Therefore we assume that the gears,
the chain and the tire move in the same direction as the foot pedal.
When the wheels are spinning it possesses angular momentum which along
with friction of the tires on the surface causes the movement of the
bicycle. We are considering the frame of the bike to be a support for
the mass, (that means the person riding the bicycle).
We are assuming the
bicycle to be on a level plain moving to the positive right hand direction.
The person pedaling the bike is supplying a constant force as long as
he pedals.
