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Quaternions are mathematical objects that extend complex numbers and can be represented as a 4-dimensional vector with scalar and vector components. Octonions are non-associative algebraic structures that are an extension of quaternions and have 8 dimensions. Both quaternions and octonions have applications in various areas of physics and computer graphics due to their properties for representing rotations and orientations.
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What are the fundamental principles and applications of quaternion physics?
Quaternion physics is a branch of physics that uses quaternions, which are mathematical entities with four components, to describe physical phenomena. Quaternions are used in various applications such as robotics, computer graphics, and quantum mechanics. The fundamental principles of quaternion physics involve understanding how quaternions can represent rotations and orientations in three-dimensional space, as well as how they can be used to perform calculations in a more efficient way compared to traditional methods.
A scalar is a quantity that has?
A scalar quantity has an angle which is an even multiple of 90 degrees. A vector quantity has an angle which is an odd multiple of 90 degrees. A quaternion has any angle and includes the scalar and the vector; quaternion q = cos(angle) + unit-vector sin(angle)
Why rotating either the coil or the magnet induces a electric current in a generator?
The simple explanation as to why a change in the coil causes a change to the electric current is that the electric field and the magnetic field are the same field and they exist in a four dimensional quaternion space.Change in a quaternion space is four dimensional and when you take the derivative there is a real derivative d/dr=d/cdt and a vector derivative DelX= d/dr + Del = d/cdt + Id/dx + Jd/dy + Kd/dz.The answer to this question is the Quaternion four space derivative of the vector Electric Field, Ev.(d/dr + Del)Ev= -Del.Ev + dEv/dr + DelxEv = -Del.Ev + dBv/dt + DelxEvThe Quaternion Derivative is X=d/dr + Del = d/cdt + DelThe vector part of the derivative dB/dt + DelxEv is the answer to the question this can be transformed by introducing the coil with dA as the area and dC as the circumference:dBv/dt.dA + DelxEv.dA = AdB/dt + Integral loop Ev.dC
A force has a magnitude of 10 newtons what other information is needed to have a complete description of its properties as a force?
No other information is needed if the force is a scalar force. Only if one believes that force is only a vector then one would need the direction information. However, it is a wrong to believe that force is only a vector. Force in general is a quaternion. A quaternion can be a scalar or a vector, thus a force can be a scalar or a vector or both. But it is cleaner to think of scalar forces as being in a single direction. Thus the direction of force is implicit, not that it does not matter. A.k.a. a scalar force is a force with an implicit direction while a vector force is a force with an explicit direction. It is cleaner to consider a scalar force as having a direction angle of a multiple of 180 degrees and a vector force having a direction angle a multiple of 90 degrees. Any other angle would be give a scalar and vector, or a quaternion. This is similar to complex numbers, there are real numbers, imaginary numbers and complex numbers. Reals and complex numbers are subsets of quaternions.
What is the difference between magnetic vector potential and magnetic scalar potential?
A vector is a quantity with both magnitude (strength) and direction. Like a force having a strength in pounds and a direction. Or a wind having magnitude (in mph) and direction (Northeast). A scalar has only magnitude. Like the length of a segment or amount of peanuts in a jar. Scalars are just numbers.
What is boson and fermion?
Bosons and Fermions are parts of Quaternion Electronic Particles. The Boson is the Quaternion Scalar part and the Fermion is the Quaternion Vector part. Quaternions are four dimensional "particles" a Boson and a three dimensional FermionThe Quaternion Unit can be described by Q= Cos(Spin) + v Sin(Spin) where v is the unit vector. The Quaternion consists of a scalar part the Boson = Cos(Spin) and a vector part the Fermion = v Sin(Spin).When the angle Spin = n pi/2 if n is a multiple of 1 then the Quaternion Unit is a positive Fermion;If n is a multiple of 2 then the Quaternion is a negative Boson;if n is a multiple of 3 then the Quaternion is a negative Fermionif n is a multiple of 4, then the Quaternion is a Positive Boson.In general Bosons are even spin angles of pi/2 and Fermions are odd spin angles of pi/2.If the spin angel is not a multiple of pi/2 then the Quaternion is the sum of a Boson and a Fermion.This looks like Complex Numbers. because it is. Complex Numbers are a Quaternion 2 dimensional subgroup with Boson and a single vector Fermions.
How you represent rgb color by quaternion in matlab?
we can represente a RGB color in matlab by a pure quaternion q=0+R*I+G*J+B*K we apply the function q=quaternion(0,R,G,B); for this you must download the qtfm toolbox.
What is the foundation of space science?
The foundation of space science is Quaternion Space and Quaternion Mathematics. A Quaternion Space , Q: Q= r + Ix + Jy + Kz = r + R = [r,R] a 4D space consisting of 1 real dimension r=ct (where c is the speed of light and t is time) and 3 vector dimensions R= Ix + Jy + Kz. Other Quaternion Quantities are: Energy W and Force and Momentum and motion are quaternion quantities. e.g. The law of gravity W = -mGm/r + mcV = [-mu/r, cmV] . A Quaternion Mathematics : A=[a,A] and B=[b,B] A+B = [a,A] + [b,B]= [a+b, A +B] AB= [a,A][b,B] = [ab - A.B, aB +Ab + AxB] A Quaternion Calculus; X= [d/dr, Del] XB= [d/dr,Del] [b,B] = [db/dr -Del.B, dB/dr + Del b + DelxB]
Can you add speed with velocity?
Yes, speed is a scalar and velocity is a vector, adding them together is called a quaternion or complex motion (s + v) = [s,v]. Complex numbers in geometry are 2 dimensional quaternion subsgroups.
What is the scientifical definition for force?
Force is the pressure of something against another object.
What does the kinetic energy and potential energy equal together?
Quaternion Energy if the Kinetic Energy is a vector energy.
What is the meaning of scalar?
In the quaternion analysis, a quantity that has magnitude, but not direction; -- distinguished from a vector, which has both magnitude and direction.
What are the fundamental principles and applications of quaternion physics?
Quaternion physics is a branch of physics that uses quaternions, which are mathematical entities with four components, to describe physical phenomena. Quaternions are used in various applications such as robotics, computer graphics, and quantum mechanics. The fundamental principles of quaternion physics involve understanding how quaternions can represent rotations and orientations in three-dimensional space, as well as how they can be used to perform calculations in a more efficient way compared to traditional methods.
Science words that starte with a q?
quartz (a type of rock) quasar quark quaternion (this is technically a mathematical term)
What is a vector quatinty?
A vector is a part of a more general number or quantity, called a Matrix or Quaternion. Vectors were developed by William Rowan Hamilton as part of a Quaternion. The Quaternion consists of a scalar part 1 and three vectors I ,J and K.. The scalar is a real number and InJ and K are vector numbers, where I^2 = J^2 = K^2 = -1.. Vectors denote directions such as an axis in space, Ix + Jy + Kz. Quaternions Q = s + V = Q(cos(Q) + Vsin(Q)) = [cos(Q), sin(Q)(I + J + K)] . The Quaternion is vector if the angle is an even multiple 90 degrees and the Quaternion is a vector when the angle is a odd multiple of 90 degrees.. If the angle is not a multiple of 90 degrees, the Quaternion is part scalar and part vector. Most variables in physics are Quaternions. ============================================ A 'vector' quantity is a quantity that has both a size and a direction. Examples are: force, velocity, acceleration, and electric field. A 'scalar' quantity is a quantity that has size but no direction. Examples are: cost, temperature, speed, and volume.
Proof or Disprove 'If every proper subgroup of G is cyclic then G must be cyclic'?
No! Take the quaternion group Q_8.
What is the identity element of the quaternion group?
If you mean in the group {1, -1, i, -i, j, -j, k, -k}, the identity element is 1.
