How perform Kinetic energy summation having matrix and vector

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Giovanni Curiazio 2022-11-6

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https://ww2.mathworks.cn/matlabcentral/answers/1844573-how-perform-kinetic-energy-summation-having-matrix-and-vector

回答： Morgan 2022-11-6

How i could calculate the following kinetic energy:

N=100

The importan thing is that:

m is a vector [N,1]

V0 is a vector [1,3]

DeltaV_c is a matrix [N,3]

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Answer 1

Morgan 2022-11-6

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So kinetic energy must always be a scalar quantity, i.e. m is a scalar, velocity is a vector but by squaring it you're finding magnitude squared which is a scalar. Making some assumptions about your question I've made a function that should help you

function KE = kineticEnergy(m,V0,DeltaV_c)
% KINETICENERGY     A function that takes mass (m) data
%                   and velocity data (V0 & DeltaV_c) to
%                   calculate total kinetic energy.
%
% Example usage: KE = KINETICENERGY(m,V0,DeltaV_c);
%
% INPUT ARGUMENTS
% ================
% m                 Mass data (size: [N,1])
% V0                Initial? velocity data (size: [1,3])
% DeltaV_c          Changed? velocity data (size: [N,3])
%
% OUTPUT ARGUMENTS
% ================
% KE                Total kinetic energy
    KE = 0.5*sum(m.*norm(V0+DeltaV_c).^2);
end

I've also created a demo file to test that the function works with random data points:

% demo_kineticEnergy.m
% Initialize MATLAB
clear variables
close all
clc
% Create Random Data Arrays
N        = 100;
m        = rand(N,1);
V0       = rand(1,3);
DeltaV_c = rand(N,3);
% Call kineticEnergy.m
KE = kineticEnergy(m,V0,DeltaV_c);