How do you find the family of orthogonal curves?

Procedure to find orthogonal trajectory

1. Let f(x,y,c)=0 be the equation of the given family of curves, where c is an arbitrary parameter.
2. Differentiate f=0; w.r.t. ‘x’ and eliminate c,ie, form a differential equation.
3. Substitute −dydx for dxdy in the above differential equation.

What is self orthogonal?

A family of curves is said to be self orthogonal if two curves of the family intersect, they intersect orthogonally.

What is an orthogonal curve?

Two (or more) intersecting curves that are perpendicular at their intersection are said to be orthogonal.

What is Cam-clay?

The Cam-Clay and modified Cam-Clay models are an elastic plastic strain hardening models that are based on Critical State theory and the basic assumption that there is a logarithmic relationship between the mean stress and the void ratio.

How do you solve orthogonal?

Definition. Two vectors x , y in R n are orthogonal or perpendicular if x · y = 0. Notation: x ⊥ y means x · y = 0. Since 0 · x = 0 for any vector x , the zero vector is orthogonal to every vector in R n .

How do you find the orthogonal line of a curve?

Two curves are said to be orthogonal if their tangent lines are perpendicular at every point of intersection. Two families of curves are said to be orthogonal if every curve in one family is orthogonal to every curve in the other family.

How do you know if your self orthogonal?

Let q be a power of an odd prime and C be a q-ary linear code. Then C is self- orthogonal if and only if c · c = 0 for all c ∈ C.

What is the use of orthogonal trajectory?

Orthogonal trajectories are used in mathematics for example as curved coordinate systems (i.e. elliptic coordinates) or appear in physics as electric fields and their equipotential curves. If the trajectory intersects the given curves by an arbitrary (but fixed) angle, one gets an isogonal trajectory.

Which curves are orthogonal?

Is Matrix orthogonal?

A square matrix with real numbers or elements is said to be an orthogonal matrix, if its transpose is equal to its inverse matrix. Or we can say, when the product of a square matrix and its transpose gives an identity matrix, then the square matrix is known as an orthogonal matrix.

What is modified cam clay?

The modified Cam-Clay model is an incremental hardening/softening elastoplastic model. Its features include a particular form of nonlinear elasticity and a hardening/softening behavior governed by volumetric plastic strain (“density” driven).

What is Hvorslev surface?

The surface of Roscoe (Hvorslev) is defined as the surface made of the last part of the set of trajectories ending to a given critical point and coming from all states of normally consolidated soils (from all states of over consolidated soils).

How the family of curves is self orthogonal?

And it is said in my text book that if the orthogonal trajectory of a curve is itself, then we say that the family of curves is self orthogonal. As an example, orthogonal trajectory of parabola Is the same function. But how this is possible? Orhogonal trajectory cut every member of given family normally.

What is the orthogonal trajectory of the family?

A curve that intersects each member of a given family of curves at right angles (orthog- onally) is called an orthogonal trajectory of the family. Each line in (c) is an orthogonal trajectory of the family of circles (a) [and conversely, each circle in (a) is an orthogonal trajectory of the family of lines (c)].

How do you know if a curve is orthogonal or perpendicular?

Two lines ℓ 1 and ℓ 2, with slopes m1 and m2, respectively, are orthogonal or perpendicular if their slopes satisfy the relationship m 1 m 2 = − 1. Two curves are orthogonal or perpendicular at a point if their respective tangent lines to the curves at that point are perpendicular.