Lagrangian Mechanics
lagrangian mechanics is the reformulation of newtonian mechanics that utilizes the lagrangian defined by
l=t-u
where
t= total kinetic energy of a system of particles
u= sum of the potential energy functions of a system of particles
in other branches of physics, the lagrangian is defined as the function
l: tq–> r
where q is the configuration sp-ce, a subset of r^3n
such that the action, defined as the functional,
a(q)= int(l) dt
when it reaches stationary value at {q(t)}, will male {q(t)} the equations of motion.
note, int() means the integration notation with the limits of integration being positive an negative infinity, respectively.
it is shown, using the calculus of variations, that the equations of motion are in such a way that they satisfy the lagrange’s equations of motion
d(d(l)/dv)-d(l)/dq=0
where d is the differential operator with respect to time, d/dx stands for partial differentiation, and v is the generalized velocity.
bob: why is general relativity so tough to learn?!
doug: cause’ you don’t know enough lagrangian mechanics!
Read Also:
- Location
the geographical point that an object is at. location, shmocation- i don’t care where definitions come from! something that’s not needed to be asked when you are writing a definition on ud location is missing.
- MATADS
an acronym, standing for “make austin take a d-mn shower”, referring to one austin m. who has a propensity for not showering. austin hasn’t taken a shower in like 10 days. dammit, matads!
- math club
the greatest club known to mankind. those that are fortunate enough to become involved get to partic-p-te in regional, statewide, and even national compet-tions. the mathletes compete against other dorks (yes, we are completely aware that we’re dorks) and spend sat-rdays with a calculator and pencil as their closest companions. great friends are made through […]
- Maury Hancock
maury is head of the theatre department and of the honor council at st. catherine’s school. he is well known for his mad directing and technical skills, uninhibited conversation, house in france, and messy office. maury is one of few faculty members at st. catherine’s who actually possess intelligence and common sense. he affectionately refers […]
- maximify
portmanteau of maximise and magnify, maxim-ify. the image on that website is pretty puny, i wanna read some detail. if i click on the thumbnail i see i can maximify it to see the full detail.