Struct ParametricDifferentiation 

pub struct ParametricDifferentiation;

Parametric differentiation operations

Implementations

impl ParametricDifferentiation

pub fn first_derivative( x_param: &Expression, y_param: &Expression, parameter: Symbol, ) -> Expression

Compute dy/dx for parametric curve with cached derivatives

Uses formula: dy/dx = (dy/dt) / (dx/dt)

Examples

use mathhook_core::simplify::Simplify;
use mathhook_core::calculus::derivatives::Derivative;
use mathhook_core::{Expression};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::ParametricDifferentiation;

let t = symbol!(t);
let x_param = Expression::function("cos", vec![Expression::symbol(t.clone())]);
let y_param = Expression::function("sin", vec![Expression::symbol(t.clone())]);
let dy_dx = ParametricDifferentiation::first_derivative(&x_param, &y_param, t);

pub fn second_derivative( x_param: &Expression, y_param: &Expression, parameter: Symbol, ) -> Expression

Compute d²y/dx² for parametric curves

Uses formula: d²y/dx² = (d/dt(dy/dx)) / (dx/dt)

Examples

use mathhook_core::{Expression};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::ParametricDifferentiation;

let t = symbol!(t);
let x_param = Expression::symbol(t.clone());
let y_param = Expression::pow(Expression::symbol(t.clone()), Expression::integer(2));
let d2y_dx2 = ParametricDifferentiation::second_derivative(&x_param, &y_param, t);

pub fn arc_length_differential( x_param: &Expression, y_param: &Expression, parameter: Symbol, ) -> Expression

Compute arc length differential

Formula: ds = √((dx/dt)² + (dy/dt)²)

Examples

use mathhook_core::simplify::Simplify;
use mathhook_core::{Expression};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::ParametricDifferentiation;

let t = symbol!(t);
let x_param = Expression::symbol(t.clone());
let y_param = Expression::pow(Expression::symbol(t.clone()), Expression::integer(2));
let arc_length_diff = ParametricDifferentiation::arc_length_differential(&x_param, &y_param, t);

pub fn curvature( x_param: &Expression, y_param: &Expression, parameter: Symbol, ) -> Expression

Compute curvature for parametric curves

Formula: κ = |x’y’’ - y’x’’| / (x’² + y’²)^(3/2)

Examples

use mathhook_core::calculus::derivatives::Derivative;
use mathhook_core::{Expression};
use mathhook_core::symbol;
use mathhook_core::calculus::derivatives::ParametricDifferentiation;

let t = symbol!(t);
let x_param = Expression::function("cos", vec![Expression::symbol(t.clone())]);
let y_param = Expression::function("sin", vec![Expression::symbol(t.clone())]);
let curvature = ParametricDifferentiation::curvature(&x_param, &y_param, t);