Show that a rocket of mass that ejects at speed (with respect to
itself) a part of its mass by time unit moves in the sense opposed
to . Give the movement law for a rocket with speed zero at time ,
located in a earth gravitational field considered as constant.
Doppler effect. Consider a light source moving at constant speed
with respect to reference frame . Using wave four-vector give
the relation between frequencies measured by an experimentator moving with
and another experimentater attached to . What about sound waves?
For a cylindrical coordinates system, metrics of the space is:
Calculate the Christoffel symbols defined by:
Consider a unit mass in a three dimensional reference frame whose metrics is:
Show that the kinetic energy of the system is:
Show that the fundamental equation of dynamics is written here (forces are
assumed to derive from a potential ) :