The proof of mass vector.
in [Math]
|
Prev: infinity ...
Next: The set of All sets
From: Ka-In Yen on 23 Nov 2005 19:56 Vector algebra was abused by physicists for hundred years. A GREAT DISASTER!!! Ka-In Yen Magnetic force: Drag nd Bernoulli force of ether dynamics. http://www.geocities.com/redlorikee Ka-In Yen wrote: > The proof of mass vector. > > Introduction: > In this paper, we will prove that linear mass density and > surface mass density are vector, and the application of mass > vector is presented. > > 1. The unit of vector. > > In physics, The unit of three-dimensional cartesian coordinate > systems is meter. In this paper, a point of 3-D coordinate > system is written as > > (p1,p2,p3) m, or (p:3) m > > and a vector is written as > > <a,b,c> m, or <a:3> m > > or > > l m<i,j,k> = <a,b,c> m > > where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, > and <i,j,k> is a unit vector which gives the direction of > the vector. > > For three reasons, a magnitude of a vector can not add to a > scalar: > i) The magnitude belongs to the set of vector; it's a > portion of a vector. Scalar belongs to a field. > ii) The magnitude is real non-negative number, but scalar > is real number. > iii) The unit of magnitude is meter, but scalar has no unit. > This is a major difference between physics and mathematics. > 5m+3 is meaningless. > > > 2. Linear mass density is a vector. > > The mass of a string is M kg, and the length of the string > is l m<i:3>. Where l m is the magnitude of the length, and > <i:3> is a 3-D unit vector which gives the direction of the > string. Then the linear mass density of the string is: > > M/(l<i:3>)=(M/l) (kg/m)<i:3> > > The direction, <i:3>, is not changed by "division", so we > can move <i:3> from denominator to numerator. A direction > is changed by -1 only. A proof is found in Clifford algebras: > > [Proof] > k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2] > =(k/l) <i,j,k> > where l is the magnitude of <a,b,c>, and <i,j,k> is the > unit vector of <a,b,c>. > [Proof] > > > 3. Surface mass density is a vector. > > A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3> > and <j:3> are unit vectors. The area vector of the parallelogram > is the cross product of these two vectors. > > l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3> > = lh abs(sin(theta)) (m^2)<k:3> > > Where theta is the angle between <i:3> and <j:3>. <k:3> is > a unit vector which is perpendicular to <i:3> and <j:3>. > For AXB=-BXA, an area has two directions. > > We can divide the area vector by the length vector. > > lh*abs(sin(theta))<k:3>/[l<i:3>] > =h<i:3>X<j:3>/<i:3> > =h(<i:3>X<j:3>)X<i:3> > (The direction, <i:3>, is not changed by "division", and > the division is replaced by a cross product.) > =-h<i:3>X(<i:3>X<j:3>) > =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)] > (where o is dot product.) > =-h(cos(theta)<i:3>-<j:3>) > =h(<j:3>-cos(theta)<i:3>) m > > The result is a rectangle, not the original parallelogram. We > can test the result. > > h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3> > > The magnitude of the area vector is conserved, but the direction > is opposite. > > The mass of a round plate is M kg, and the area vector is > A m^2<i:3>; then the surface mass density is > > M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3> > > > 4. Mass vector in physics. > > Mass vector has been found in two equations: 1) the velocity > equation of string. 2) Bernoulli's equation. > > i) For waves on a string, we have the velocity equation: > > v=sqrt(tau/mu). v is velocity of wave, tau is tension > applying to string, and mu is linear mass density of > string. We can rewrite the equation: > > mu=tau/v^2. > > In the above equation, the mu is parallel to tau, and both > of them are vector. > > ii) Bernoulli's equation is: > > P + k*v^2/2=C (P is pressure, k is volume density, and v is > velocity. Here we neglect the gravitational term.) > > Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's > equation(where <i:3> is a unit vector), > > P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3> > F<i:3> + L<i:3>*v^2/2=C*A<i:3> > (where F is the magnitude of force, and L is the magnitude > of linear mass density.) > > These two equations are well used in the theory "Magnetic force: > Combining Drag force and Bernoulli force of ether dynamics." > For detail, please refer to my site: > http://www.geocities.com/redlorikee
From: Ka-In Yen on 29 Nov 2005 21:06 Eric Gisse wrote: > Ka-In Yen wrote: > > The proof of mass vector. > > Introduction: > > In this paper, we will prove that linear mass density and > > surface mass density are vector, and the application of mass > > vector is presented. > > > > ii) Bernoulli's equation is: > > > > P + k*v^2/2=C (P is pressure, k is volume density, and v is > > velocity. Here we neglect the gravitational term.) > > These are all scalar quantities. > Dear Eric, Thank you for your comment. P(pressure) = F(force) / A(area) F and A are two vectors being parallel to each other, and P is a scalar quantity. Please refer to: http://www.grc.nasa.gov/WWW/K-12/airplane/pressure.html A parallelepiped with three vectors A,B,C form adjacent edges, and the volume of the parallelepiped is V=abs( Ao(BXC) ). o is dot product, and X is cross product. V is a scalar quantity. Vd(volume density) = M(mass) / V(volume) M, V, and Vd are scalar quantities. Ka-In Yen Magnetic force: Drag force and Bernoulli force of ether dynamics. http://www.geocities.com/redlorikee > > > > Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's > > equation(where <i:3> is a unit vector), > > > > P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3> > > F<i:3> + L<i:3>*v^2/2=C*A<i:3> > > (where F is the magnitude of force, and L is the magnitude > > of linear mass density.)
From: yen, ka-in on 1 Dec 2005 21:55 Einstein was ill-trained on three dimensional vector space; the fourth dimension was suggested by him. A BLOODY JOKE!!! Ka-In Yen Magnetic force: Drag and Bernoulli force of ether dynamics. http://www.geocities.com/redlorikee Ka-In Yen wrote: > The proof of mass vector. > > Introduction: > In this paper, we will prove that linear mass density and > surface mass density are vector, and the application of mass > vector is presented. > > 1. The unit of vector. > > In physics, The unit of three-dimensional cartesian coordinate > systems is meter. In this paper, a point of 3-D coordinate > system is written as > > (p1,p2,p3) m, or (p:3) m > > and a vector is written as > > <a,b,c> m, or <a:3> m > > or > > l m<i,j,k> = <a,b,c> m > > where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, > and <i,j,k> is a unit vector which gives the direction of > the vector. > > For three reasons, a magnitude of a vector can not add to a > scalar: > i) The magnitude belongs to the set of vector; it's a > portion of a vector. Scalar belongs to a field. > ii) The magnitude is real non-negative number, but scalar > is real number. > iii) The unit of magnitude is meter, but scalar has no unit. > This is a major difference between physics and mathematics. > 5m+3 is meaningless. > > > 2. Linear mass density is a vector. > > The mass of a string is M kg, and the length of the string > is l m<i:3>. Where l m is the magnitude of the length, and > <i:3> is a 3-D unit vector which gives the direction of the > string. Then the linear mass density of the string is: > > M/(l<i:3>)=(M/l) (kg/m)<i:3> > > The direction, <i:3>, is not changed by "division", so we > can move <i:3> from denominator to numerator. A direction > is changed by -1 only. A proof is found in Clifford algebras: > > [Proof] > k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2] > =(k/l) <i,j,k> > where l is the magnitude of <a,b,c>, and <i,j,k> is the > unit vector of <a,b,c>. > [Proof] > > > 3. Surface mass density is a vector. > > A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3> > and <j:3> are unit vectors. The area vector of the parallelogram > is the cross product of these two vectors. > > l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3> > = lh abs(sin(theta)) (m^2)<k:3> > > Where theta is the angle between <i:3> and <j:3>. <k:3> is > a unit vector which is perpendicular to <i:3> and <j:3>. > For AXB=-BXA, an area has two directions. > > We can divide the area vector by the length vector. > > lh*abs(sin(theta))<k:3>/[l<i:3>] > =h<i:3>X<j:3>/<i:3> > =h(<i:3>X<j:3>)X<i:3> > (The direction, <i:3>, is not changed by "division", and > the division is replaced by a cross product.) > =-h<i:3>X(<i:3>X<j:3>) > =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)] > (where o is dot product.) > =-h(cos(theta)<i:3>-<j:3>) > =h(<j:3>-cos(theta)<i:3>) m > > The result is a rectangle, not the original parallelogram. We > can test the result. > > h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3> > > The magnitude of the area vector is conserved, but the direction > is opposite. > > The mass of a round plate is M kg, and the area vector is > A m^2<i:3>; then the surface mass density is > > M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3> > > > 4. Mass vector in physics. > > Mass vector has been found in two equations: 1) the velocity > equation of string. 2) Bernoulli's equation. > > i) For waves on a string, we have the velocity equation: > > v=sqrt(tau/mu). v is velocity of wave, tau is tension > applying to string, and mu is linear mass density of > string. We can rewrite the equation: > > mu=tau/v^2. > > In the above equation, the mu is parallel to tau, and both > of them are vector. > > ii) Bernoulli's equation is: > > P + k*v^2/2=C (P is pressure, k is volume density, and v is > velocity. Here we neglect the gravitational term.) > > Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's > equation(where <i:3> is a unit vector), > > P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3> > F<i:3> + L<i:3>*v^2/2=C*A<i:3> > (where F is the magnitude of force, and L is the magnitude > of linear mass density.) ....
From: Ka-In Yen on 8 Dec 2005 19:49 Dear PD, Eric Gisse, Do you have any further questions? Ka-In Yen Magnetic force: Drag and Bernoulli force of ether dynamics http://www.geocities.com/redlorikee Ka-In Yen wrote: > The proof of mass vector. > > Introduction: > In this paper, we will prove that linear mass density and > surface mass density are vector, and the application of mass > vector is presented. > > 1. The unit of vector. > > In physics, The unit of three-dimensional cartesian coordinate > systems is meter. In this paper, a point of 3-D coordinate > system is written as > > (p1,p2,p3) m, or (p:3) m > > and a vector is written as > > <a,b,c> m, or <a:3> m > > or > > l m<i,j,k> = <a,b,c> m > > where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, > and <i,j,k> is a unit vector which gives the direction of > the vector. > > For three reasons, a magnitude of a vector can not add to a > scalar: > i) The magnitude belongs to the set of vector; it's a > portion of a vector. Scalar belongs to a field. > ii) The magnitude is real non-negative number, but scalar > is real number. > iii) The unit of magnitude is meter, but scalar has no unit. > This is a major difference between physics and mathematics. > 5m+3 is meaningless. > > > 2. Linear mass density is a vector. > > The mass of a string is M kg, and the length of the string > is l m<i:3>. Where l m is the magnitude of the length, and > <i:3> is a 3-D unit vector which gives the direction of the > string. Then the linear mass density of the string is: > > M/(l<i:3>)=(M/l) (kg/m)<i:3> > > The direction, <i:3>, is not changed by "division", so we > can move <i:3> from denominator to numerator. A direction > is changed by -1 only. A proof is found in Clifford algebras: > > [Proof] > k/<a,b,c>=[k<a,b,c>]/[<a,b,c>^2] > =(k/l) <i,j,k> > where l is the magnitude of <a,b,c>, and <i,j,k> is the > unit vector of <a,b,c>. > [Proof] > > > 3. Surface mass density is a vector. > > A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3> > and <j:3> are unit vectors. The area vector of the parallelogram > is the cross product of these two vectors. > > l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3> > = lh abs(sin(theta)) (m^2)<k:3> > > Where theta is the angle between <i:3> and <j:3>. <k:3> is > a unit vector which is perpendicular to <i:3> and <j:3>. > For AXB=-BXA, an area has two directions. > > We can divide the area vector by the length vector. > > lh*abs(sin(theta))<k:3>/[l<i:3>] > =h<i:3>X<j:3>/<i:3> > =h(<i:3>X<j:3>)X<i:3> > (The direction, <i:3>, is not changed by "division", and > the division is replaced by a cross product.) > =-h<i:3>X(<i:3>X<j:3>) > =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)] > (where o is dot product.) > =-h(cos(theta)<i:3>-<j:3>) > =h(<j:3>-cos(theta)<i:3>) m > > The result is a rectangle, not the original parallelogram. We > can test the result. > > h(<j:3>-cos(theta)<i:3>)Xl<i:3>=lh m^2<j:3>X<i:3> > > The magnitude of the area vector is conserved, but the direction > is opposite. > > The mass of a round plate is M kg, and the area vector is > A m^2<i:3>; then the surface mass density is > > M kg/(A m^2<i:3>)=M/A (kg/m^2)<i:3> > > > 4. Mass vector in physics. > > Mass vector has been found in two equations: 1) the velocity > equation of string. 2) Bernoulli's equation. > > i) For waves on a string, we have the velocity equation: > > v=sqrt(tau/mu). v is velocity of wave, tau is tension > applying to string, and mu is linear mass density of > string. We can rewrite the equation: > > mu=tau/v^2. > > In the above equation, the mu is parallel to tau, and both > of them are vector. > > ii) Bernoulli's equation is: > > P + k*v^2/2=C (P is pressure, k is volume density, and v is > velocity. Here we neglect the gravitational term.) > > Multiplying cross area vector A m^2<i:3> of a string to Bernoulli's > equation(where <i:3> is a unit vector), > > P*A<i:3> + k*A<i:3>*v^2/2=C*A<i:3> > F<i:3> + L<i:3>*v^2/2=C*A<i:3> > (where F is the magnitude of force, and L is the magnitude > of linear mass density.) > > These two equations are well used in the theory "Magnetic force: > Combining Drag force and Bernoulli force of ether dynamics." > For detail, please refer to my site: > http://www.geocities.com/redlorikee
From: Ka-In Yen on 30 Dec 2005 22:24
Ka-In Yen wrote: > The proof of mass vector. > > Introduction: > In this paper, we will prove that linear mass density and > surface mass density are vector, and the application of mass > vector is presented. > > 1. The unit of vector. > In physics, The unit of three-dimensional cartesian coordinate > systems is meter. In this paper, a point of 3-D coordinate > system is written as > (p1,p2,p3) m, or (p:3) m > and a vector is written as > <a,b,c> m, or <a:3> m > or > l m<i,j,k> = <a,b,c> m > where l=abs(sqrt(a^2+b^2+c^2)) is the magnitude of the vector, > and <i,j,k> is a unit vector which gives the direction of > the vector. > > 3. Surface mass density is a vector. > A parallelogram has two vectors: l m<i:3> and h m<j:3>. <i:3> > and <j:3> are unit vectors. The area vector of the parallelogram > is the cross product of these two vectors. > l m<i:3> X h m<j:3>= lh (m^2 )<i:3>X<j:3> > = lh abs(sin(theta)) (m^2)<k:3> > Where theta is the angle between <i:3> and <j:3>. <k:3> is > a unit vector which is perpendicular to <i:3> and <j:3>. > For AXB=-BXA, an area has two directions. > We can divide the area vector by the length vector. > lh*abs(sin(theta))<k:3>/[l<i:3>] > =h<i:3>X<j:3>/<i:3> > =h(<i:3>X<j:3>)X<i:3> > (The direction, <i:3>, is not changed by "division", and > the division is replaced by a cross product.) > =-h<i:3>X(<i:3>X<j:3>) > =-h[<i:3>(<i:3>o<j:3>)-<j:3>(<i:3>o<i:3>)] > (where o is dot product.) > =-h(cos(theta)<i:3>-<j:3>) > =h(<j:3>-cos(theta)<i:3>) m > The result is a rectangle, not the original parallelogram. In the above, the "area vector division by length vector" is suggested. We can divide a length vector by a velocity in a different way. Assuming a length vector is l m<i:3>, and a velocity is v (m/s) <j:3>. <i:3> and <j:3> are unit vectors. l m<i:3> / [ v (m/s) <j:3> ] =l <i:3>o<j:3> / v s <j:3> is moved to numerator. o is dot product. =l cos(theta) / v s ---------(1) theta is the angle between two vectors. OR v (m/s)<j:3> / [ l m<i:3> ] =v cos(theta) / l s^(-1) --------(2) Both length vector and area vector have two directions; we can choose one of their directions to keep cos(theta)>0. (1)*(2)=(cos(theta))^2 (The result is not 1.) We can caculate pressure=force/area with same method. Ka-In Yen Magnetic force: Drag and Bernoulli force of ether dynamics. http://www.geocities.com/redlorikee |