What is Galilean transformation: Definition and 55 Discussions
In physics, a Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group. The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. In special relativity the homogenous and inhomogenous Galilean transformations are, respectively, replaced by the Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations.
The equations below are only physically valid in a Newtonian framework, and not applicable to coordinate systems moving relative to each other at speeds approaching the speed of light.
Galileo formulated these concepts in his description of uniform motion.
The topic was motivated by his description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth.
Hi, Penrose in his book "The Road to Reality" claims that Newton/Galilean spacetime has actually a structure of fiber bundle. The base is one-dimensional Euclidean space (time) and each fiber is a copy of ##\mathbb E^3##. The projection on the base space is the "universal time mapping" that...
The LT can be derived from the first postulate of SR, assuming linearity an that velocity composition is commutative, and that GT can be excluded: ##t' \neq t##.
Definition of the constant velocity ##v##:
##x' = 0 \Rightarrow x-vt=0\ \ \ \ \ \ ##(1)
With assumed linearity follows for the...
I have a quick question about the Galilean transform. If I have Alice running and Bob stationary. The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position.
If I want Bob...
It's frequently discussed Galilean transformation brings one inertial frame to another inertial frame, and such a transformation leaves Newton's second law invariant (of the same form). I wonder what happens for non-inertial frame? If we start with a non-inertial frame, and Galilean transform...
I know we can prove that a Galilean transformation sends one inertial frame to another inertial frame, by proving ##\frac{d^2 f(\vec{r})}{d(f(t))^2} = \frac{d^2 \vec{r}}{dt^2}##, but can we prove the reverse? Can we prove that if the acceleration seen in two frames are the same, then the...
Here's what I did so far.
The velocity of the first car is ##v = v_0 +at##
Frame of reference S = the road
Frame of reference S' = the second car
thus, v' is the speed of the first car in the frame of reference S' and v the speed in the frame of reference S.
Here's what make me doubt.
The...
I got a bit confused, and hoped someone could clarify a few things. As far as I am aware, a change of basis is an identity transformation ##I_V## on the vector space (pg. 113) and we can write the relationship between the components of some vector ##v## in the different bases ##\beta## and...
(1) Uniformly moving frames
I begin with a drawing of the situation. The events are labelled as ##\color{red}{E_1}## and ##\color{red}{E_2}##. We note the time of those events : ##t_1 = t'_1 = 30s## and ##t_2 = t_2' = 30+60 = 90s##.
I attempt the problem in two different ways.
(a) By...
I'm reading the article https://www.researchgate.net/publication/267938119_ON_THE_GALILEAN_COVARIANCE_OF_CLASSICAL_MECHANICS (pdf link here), in which the authors want to establish the transformation rule for momentum, assuming only that ##\vec{F}=d\vec{p}/dt## and notwithstanding the relation...
Homework Statement
Two objects ##1## and ##2## move at constant speeds ##v_1## and ##v_2## along of two mutually perpendicular lines. At the moment ##t = 0## the particles are located at distances ##l_1## and ##l_2## from the point of intersection of the lines. At what time will the two objects...
Homework Statement
I am having a issue relating part of this question to the Galilean transformation.
Question
Relative to the laboratory, a rod of rest length ##l_0## moves in its own line with velocity u. A particle moves in the same line with equal and opposite velocity . How long dose it...
Homework Statement
$$\Psi = Ae^{\frac{i}{\hbar}(px-\frac{p^2}{2m}t)}$$
where ##p = \hbar k## and ##E = \hbar \omega = \frac{p^2}{2m}## for a nonrelativistic particle.
Find ##\Psi'(x',t')##, E' and p', under a galilean tranformation.
Homework Equations
$$\Psi'(x',t') = f(x,t)\Psi(x,t)$$
where...
The Galilean transformations are simple.
x'=x-vt
y'=y
z'=z
t'=t.
Then why is there so much jargon and complication involved in proving that Galilean transformations satisfy the four group properties (Closure, Associative, Identity, Inverse)? Why talk of 10 generators? Why talk of rotation as...
Is the attached solution complete? In particular, do we need to prove that ##V'(r_{12}')=V(r_{12})##, where ##V'(r_{12}')## is the potential energy function in the reference frame ##S'##, moving at a uniform velocity with respect to the reference frame ##S##, and ##r_{12}'## is the distance...
For using Galilean transformation, I have to assume that speed of light w.r.t. ether frame is c.
W.r.t. ether frame,
E = E0 eik(x-ct)
W.r.t. S' frame which is moving with speed v along the direction of propagation of light,
E' = E0 eik(x'-c't')
Under Galilean transformation,
x' = x-vt,
t' = t...
Hello everyone,
I am confused with the minus sign of x'=x-vt. When there are 2 references frames called K and K' which K is at rest and K' moves to right with velocity V with respect to K. Let there is another frame which is my frame of reference called O. The vector sum of the displacement...
Homework Statement
Write the Galilean coordinate transformation equations
for the case of an arbitrary direction for the relative velocity v of one frame with respect to the other. Assume that the corresponding axes of the two frames remain parallel. (Hint: let v have componentsvx, vy, vz.)...
Homework Statement
2. The attempt at a solution
3. Relevant equations
In the first problems of that book i was using the Galilean transformations where
V1 = V2 + V
But if i use that then
V1 = 0.945 - 0.6
V1 = 0.345
Is not the same result, so I am confused.
In this new problems we are...
The D'Alembert equation for the mechanical waves was written in 1750. It is not invariant under a Galilean transformation.
Why nobody was shocked about this at the time? Why we had to wait more than a hundred years (Maxwell's equations) to discover that Galilean transformations are wrong...
What was the need for Lorentz transformation in pre-relativity period?
Why was it necessary for the velocity of light to be invariant between different inertial frames and hence what was the need for Lorentz transformation when it was believed that velocity of light was constant with respect to...
As the title says, is energy Galilean invariant?
I'm fairly sure it isn't, since if one considers the simple case of a free particle, such that its energy is ##E=\frac{p^{2}}{2m}##, then under a Galilean boost, it follows that ##E'=...
I'm getting quite stuck on this problem here.
Galileo said that Xb = Xa - V*Ta.
(This follows from dv = dx/t --> Xa - Xb = t*dv --> the above formula)
Thus, it is concluded Xa = Xb + V*Ta, but why?
In my thought experiment the objects are moving relative to each other,
thus if A is moving away...
The Galilean transforms for rotations, boosts and translations in 2D are the follows:
Rotations:
x' = xcosθ + ysinθ
y' = -xsinθ + ycosθ
Boosts:
x' = x - vxt
y' = y - vyt
Translations:
x' = x - dx
y' = y - dx
I wanted to combine these into a single pair of equations, so my first thought was...
Homework Statement
A 52kg man is on a ladder hanging from a balloon that has a total mass of 450kg (including the basket passenger). The balloon is initially stationary relative to the ground. If the man on the ladder begins to climb at 1.2m/s relative to the ladder, (a) in what direction does...
Homework Statement
Given a reference frame O' moving at a constant speed $\vec{V}$ in relation to another reference frame O, I want to prove that
##\vec{r_{1B}} \times m_1\vec{v_{1B}} + \vec{r_{2B}} \times m_2\vec{v_{2B}} = \vec{r_{1F}} \times m_1\vec{v_{1F}} + \vec{r_{2F}} \times...
I'm currently collating my own personal notes and would really appreciate some feedback on my description of the relativity of position and velocity in classical mechanics. Here is what I have written
"Position is clearly a relative quantity as two inertial frames S and S' displaced by a...
I'm a little bit confused about the relationship between Galileo's Principle of Relativity and Newton's Laws. Indeed, as I understand, the Galilean Principle of Relativity is what Galileo presented with Salviatti's ship discussion. The discussion seems to lead to a simple idea: "if one performs...
Hello people,
I have a question regarding the x' component in the Lorentz/Galilean transformation.
So from what i understand is that there are 2 coordinate systems used in the transformations. One is used as a reference point and one is used for moving away from this point. The moving away in...
Homework Statement
Consider Newton’s force law for two particles interact through a central force F12(r1',r2',u1,u2), where by Newton’s third law F12 = -F21.
m1(d^2r1/dt^2) = F12(r1,r2,u1,u2)
m2(d^2r2/dt^2) = F21(r1,r2,u1,u2)
A. Show that Newtonian mechanics is form invariant with respect...
Homework Statement
Consider Newton’s force law for two particles interact through a central force F12(r1',r2',u1,u2), where by Newton’s third law F12 = -F21.
m1(d^2r1/dt^2) = F12(r1,r2,u1,u2)
m2(d^2r2/dt^2) = F21(r1,r2,u1,u2)
A. Show that Newtonian mechanics is form invariant with respect to...
r\rightarrow r-2qz and \psi\rightarrow\psi+q\cdot(r-qz), I don't know how to derive it, anybody know?
This question results from the book "Optical Solitons: From Fibers to Photonic Crystals [1 ed.]" section 6.5
I'm currently taking a modern physics course, I came across this problem which really threw me off guard:
Three spaceships A, B, and C are in motion as shown in the figure. The commander on ship B observes ship C approaching with a relative velocity of 0.83c. The commander also observes ship A...
Recently, I've been pondering deeply on relativity (both Galilean and SR) and all of a sudden I find that I don't grasp even the basic concepts of physics (or life) anymore, i.e. I can't go back to my previous, "normal" mode of thinking.
Consider Newtonian mechanics, take the ground to be at...
Homework Statement
A girl is riding a bicycle along a straight road at constant speed, and passes a friend standing at a bus stop (event #1). At a time of 60 s later the friend catches a bus (event #2)
If the distance separating the events is 126 m in the frame of the girl on the bicycle...
I'm still having trouble with the basic foundations of relativity so I am taking a look here at the Galilean transformation.
I know the only thing that changes is
x' = x-vt
Now can someone explain what each variable stands for and can show me how you would do an actual example with...
Hi everyone,
Homework Statement
I have a mass like in the drawing and a moving cart with constant acceleration. The potential (also in the drawing) is given as V=A4x^{4}
I want to calculate the frequency of the oscillation of the mass as a function of the acceleration when the cart is...
Hi! I was reading some notes on relativity (Special relativity) (http://teoria-de-la-relatividad.blogspot.com/2009/03/3-la-fisica-es-parada-de-cabeza.html) and it says that the classical wave equation is not Galilean Invariant. I tried to show it by myself, but I think there is some point that...
Homework Statement
Conventionally, the Galilean Transformation relates two reference frames that begin at the same location and time with one reference frame moving at a constant velocity {\vec{v}} along a positive {x}-axis (which is common to both reference frames) with respect to the other...
in a 1 d system.
x measured WRT an inertial frame k, are the following, valid Galilean transformations:
x=x'- sin(wt)
and
x=x'3Not sure where to go with this...
I can't find any relevant material anywhere.
Homework Statement
In a Summer's day, there's no wind, and start to rain. So the drops fall vertically for an observer on the ground. A car has a velocity of 10 Km/h and the driver see that the drops are coming perpendicularly to the windshield. If 60° is the angle between the windshield and...
hi... I´m attending a course of advanced classical mechanics.
I´m working on statistical mechanics, so I´m not so familiar with some things on the course.
I must solve the follwing problem for homework:
show that every galilean transformation g on the (galilean space, using natural...
Homework Statement
a railcart A moves in a fixed accelaration a_1=a_1 \hat{x} (a_1 is relavive to earth) at moment t=0 a ball is thrown from it in the velocity v_0 (v_0 is relative to the railcart A) and with the angle \alpha above the horizon. the velocity of the railcart when the ball...
Homework Statement
Pilots are racing small, relatively high-powered airplanes arounds courses marked by a pylon on the ground at each end of the course. Suppose two such evenly matched racers fly at airspeeds of 130 mi/h. Each flies one complete round tripof 25 miles, but their courses are...
Homework Statement
1) Show that the electromagnetic wave equation,
d^2(phi)/dx^2 + d^2(phi)/dy^2 + d^2(phi)/dz^2 –(1/c^2)( d^2(phi)/dt^2) = 0
is not invariant under Galilean transformation.
Note: here d is a partial differential operator.
Homework Equations...
i have trouble taking the equations given, that is the conversion of one coordinate frame to another.
lets assume at the starting point there are two observers (coordinates (x,y,z,t)).
one observer moves in the x direction and the other observer stays still. the observer that moves has the...