Kāore e taea te wehewehe i te matapaki i ngā whārite i roto i te pāngarau me te matapaki i te pūnaha taunga Cartesian. Ko te pūnaha taunga Cartesian te pūnaha e whakamahia whānuitia ana mō te whakatauira me te tātari i ngā āhuatanga rerekē i roto i te wāhi rua-ahu me te toru-ahu. I roto i tēnei tuhinga, ka tūhuratia e mātou te ariā o ngā whārite ōrite i roto i te horopaki o te pūnaha taunga Cartesian.
He Kupu Whakataki ki ngā Wētera i roto i te Pūnaha Taunga Cartesian
I roto i te pūnaha taunga Cartesian, ka taea te whakaatu i ia pūwāhi i roto i te wāhi rua-ahu hei takirua raupapa (x, y), ko x te taunga whakapae, ko y te taunga poutū. Mō te wāhi toru-ahu, kei a tātou te toru-āhua (x, y, z). Ko te whārite i roto i tēnei horopaki he hinonga pāngarau kei a ia te rahi (te roa rānei) me te ahunga.
Ko te ira i roto i te wāhi ahu-rua ka whakaaturia ko \(\vec{v}\) = (v_x, v_y), ko \(v_x\) me \(v_y\) ngā wāhanga o te ira i te tuaka-x me te tuaka-y. I roto i te wāhi ahu-toru, ka whakaaturia te ira ko \(\vec{v}\) = (v_x, v_y, v_z).
Te Ariā o te Taurite Wekita
E kiia ana he ōrite ngā whārite e rua mēnā he ōrite te rahi me te ahunga, ahakoa te tīmatanga. I roto i ngā kupu pāngarau, e kiia ana he ōrite ngā whārite e rua \(\vec{u}\) = (u_x, u_y) me \(\vec{v}\) = (v_x, v_y) mēnā:
1. \(u_x = v_x\)
2. \(u_y = v_y\)
Ko te tikanga, kāore ngā whārite e herea ki tētahi pūwāhi tīmatanga motuhake. Ka taea te whakanoho i ngā whārite e rua ki ngā wāhi katoa o te wāhi, engari ki te rite te ahunga me te rahi o rāua, ka kiia tonu rāua he ōrite, he ōrite rānei. He āhuatanga matua tēnei e hanga ana i ngā whārite hei taputapu maha-whakamahinga i roto i te pāngarau me te ahupūngao.
Te Whakatairite Āhuahanga
Me kī he rua ā tātou whārite \(\vec{u}\) = (3, 4) me \(\vec{v}\) = (3, 4). Ina tirohia ēnei whārite e rua i roto i te pūnaha taunga Cartesian, ka tohu i ngā pere kei te ahunga kotahi, ā, he rite te roa, ahakoa ka tīmata mai i ngā pūwāhi rerekē. Nō reira, ki te tuhia e tātou \(\vec{u}\) mai i te pūtake (0, 0) ki te pūwāhi (3, 4) me \(\vec{v}\) mai i tētahi pūtake rerekē, hei tauira (1, 1), ki te pūwāhi (4, 5), he ōrite tonu ēnei whārite e rua nā te mea he rite te ahunga me te rahi.
Te Whakaaturanga Wetereo ōrite i roto i te Pāngarau
I roto i te pāngarau, ka whai ngā whārite ōrite i te mātāpono e whai ake nei:
– Mena he whārite te \(\vec{v}\) = (v_x, v_y), ka taea te whiwhi i tētahi whārite e ōrite ana ki te \(\vec{v}\) mā te tāpiri i te whārite whakawhiti kotahi ki ōna pūwāhi tīmatanga me ōna pūwāhi mutunga.
– I roto i te āhua whānui, mēnā he rite ngā whārite e rua o \(\vec{v_1}\) = (v_{1x}, v_{1y}) me \(\vec{v_2}\) = (v_{2x}, v_{2y}), kātahi ka noho he whārite pumau \(\vec{k}\) = (k_x, k_y) kia penei:
\[
\vec{v_1} = \vec{v_2} + \vec{k} – \vec{k}
\]
E mau ana tēnei ōwehenga i roto i te wāhi ahu-n, ā, e whakanui ana i te meka ko ngā whārite te kaupapa matua o ngā rerekētanga o ngā tūranga, ehara i te mea ko ngā tūranga tonu.
Te Whakamahinga o ngā Wēka Taurite i roto i te Ahupūngao
I roto i te ahupūngao, he mea nui te ariā o ngā whārite ōrite, inā koa i roto i te tātaritanga o te kaha, te tere, me te nekehanga. Hei tauira, ka taea te whakamaori i ngā kaha e mahi ana i tētahi pūwāhi i roto i tētahi mea (hei whārite ōrite) mēnā ka puta he pānga ōrite i runga i te whakaterenga rārangi, i te huringa rānei o te nekehanga.
Ngā Tauira Taupānga:
1. Ngā Kaha me ngā Waehere Taurite:
I roto i te hangarau matarohia, mēnā ka whakaaturia te kaha F hei whārite, ā, ka whakamahia ki tētahi pūwāhi ki runga i tētahi mea, ka taea e tātou te neke i te pūwāhi e whakamahia ana te kaha mā te tawhiti ōrite. He mea nui tēnei i roto i te tatau i ngā wā o te kaha, i ngā taipana rānei, ina whakamahia ngā wāhanga kaha ōrite hei whakaoti rapanga mīhini.
2. Tere:
Ko te tere hei whārite e whakaatu ana i te ahunga me te tere o te nekehanga o tētahi mea. Hei tauira, ko te tere o tētahi motuka e neke ana ki te rawhiti i te 60 km/h ka taea te whakaatu hei whārite (60, 0) mēnā ka tohu te tuaka-x ki te rawhiti. Ka whakaahuahia e ngā whārite ōrite katoa ngā āhuatanga nekehanga ōrite, ahakoa he rerekē ō rātou pūwāhi tīmatanga, hei tauira, (1, 1) ki (61, 1).
Ngā Taurite Taurite me ngā Wetere Taurite
I roto i te wāhi toru-ahu, he maha tonu tā mātou whakamahi i ngā taunga ōrite hei whakawhānui ake i tā mātou tātari. Ka whakauruhia e tēnei pūnaha te taunga whakaatu kaiwhakahaere matihiko, e whānui ake ai tō mātou māramatanga ki ngā whārite ōrite. He maha tonu te whakamahinga o ngā taunga ōrite i roto i ngā whakairoiro rorohiko hei whakahaere i ngā panonitanga āhuahanga pērā i ngā hurihanga, ngā whakawhiti, me te tauine. I roto i tēnei horopaki, ka taea e ngā whārite ōrite te mahi i ngā whakarerekētanga ōrite me te huatau ki ngā taunga Cartesian.
Whakamutunga
Ko ngā whārite ōrite i roto i te pūnaha taunga Cartesian he ariā taketake e hanga ana i te pūtake o ngā tono maha o te pāngarau me te ahupūngao. Ko te mārama ki tēnei ariā ko te mōhio he ōrite ngā whārite e rua mēnā he rite te ahunga me te rahi, ahakoa he rerekē pea ō rāua tīmatanga. Ko te whakaaturanga pāngarau o ngā whārite ōrite e whakaatu ana ka taea e tēnei āhuatanga te neke i ngā tīmatanga me ngā mutunga o ngā whārite me te kore e whakarerekē i ō rāua āhuatanga taketake.
Ko te whakamahinga o tēnei ariā i roto i ngā momo mara, pērā i te ahupūngao, e whakanui ana i te hiranga o te mārama ki te ariā whārite hei tātaritanga atu. I te ao tūturu, mā te ariā o ngā whārite ōrite ka taea te tatau māmā ake i ngā kaha, ngā tere, me te maha atu o ngā āhuatanga o te miihini me te kinematics.
Mā te āheinga ki te whakaatu me te whakahaere i ngā whārite i roto i tētahi pūnaha taunga Cartesian, ka taea e tātou te whakatauira me te tātari i te whānuitanga o ngā āhuatanga me ngā pūnaha uaua me te tino tika me te tika. Nā tēnei ka waiho te ariā o ngā whārite ōrite hei kaupapa nui, hei kaupapa whakamīharo hoki i roto i te ako i te pāngarau me te ahupūngao.
