MHB Degree of Freedom: Maths Definition & Differential Equations

AI Thread Summary
The degree of freedom in mathematics, particularly in differential equations, refers to the number of independent values that can be chosen in a problem. This concept varies based on the specific scenario being analyzed. For instance, a bead on a circular frame has one degree of freedom due to the dependency between its x and y coordinates. In contrast, a point on a plane has two degrees of freedom, while a point in three-dimensional space has three. Additionally, a projectile's trajectory in three-dimensional space is considered one-dimensional since its position is determined by a single variable, time.
anum
Messages
6
Reaction score
0
what is meant by the degree of freedom in Mathematics? Especially in the differential equations.
 
Mathematics news on Phys.org
It depend a lot on the specific problem. Generally, "the degrees of freedom" are the number of values that can be arbitrarily, and independently, chosen in a problem. For example, if you have a bead moving on a circular frame, each point has an (x, y) coordinate but since the point must lie on a circle, x and y are not independent- given either x or y we can calculate the other so this problem has one degree of freedom. A point that can lie anywhere on a given plane has three two degrees of freedom because a plane is two dimensional. A point that can be anywhere in three dimensional space has three degrees of freedom. On the other hand, a "projectile" problem, where an object is launched along some trajectory in three dimensional space is one dimensional since the (x, y, z) position of the projectile is determined by the single variable, t, the time.
 
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
Back
Top